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History of the Calendar 

in Different Countries Through the Ages 

M.N. Saha 

N.C. Lahiri 

Rafi Marg, New Delhi- 1 10001 

Part C of Report of Calendar Reform Committee, 
Government of India 

First published: 1955 
Reprinted: 1992 

© Council of Scientific & Industrial Research, New Delhi 

Printed by Publications & Information Directorate 
Dr K.S. Krishnan Marg, New Delhi -110012 


The Council of Scientific & Industrial Research (CSIR) of the Government of India appointed a Calendar 
Reform Committee under the chairmanship of Prof. Meghnad Saha in November 1952. The Committee was 
entrusted with the task of 'examining all the existing calendars which are being followed in the country at 
present and after a scientific study of the subject, submit proposals for an accurate and uniform calendar for 
the whole of India'. The following were the members of the Committee: 

Prof. M.N. Saha, D.Sc, RR.S., M.P. (Chairman) 

Prof. A.C. Banerji, Vice-Chancellor, Allahabad University 

Dr. K.L. Daftari, Nagpur 

Shri J.S. Karandikar, Ex-Editor, The Kesari, Poona 
Dr. Gorakh Prasad, D.Sc., Allahabad University 
Prof. R.V. Vaidya, Madhav College, Ujjain 
Shri N.C. Lahiri, Calcutta (Secretary) 

Dr. Gorakh Prasad and Shri N.C. Lahiri came in place of Prof. S.N. Bose and Dr. Akbar Ali who were 
originally appointed but were unable to serve. 

The Committee's Report was submitted to CSIR in 1955 and the Government, in accepting the recom- 
mendations of the Committee, decided that 'a unified National Calendar' (the Saka Calendar) be adopted for 
use with effect from 21 March 1956 A.D., i.e., 1 Chaitra 1878 Saka. The Report of the Calendar Reform 
Committee was published by CSIR in 1955. Part C of the Report consisting of a review of 'History of the 
calendar in different countries through the ages' by Prof. M.N. Saha and Shri N.C. Lahiri was also published 
separately. This useful publication has been out of print for some time and scientists in general, and 
astronomers in particular, have been conscious of the non-availability of this valuable review. Therefore, the 
CSIR has decided to reprint it. No changes have been made from the original except that 'Corrigenda and 
Addenda' have been incorporated into the text, and consequently the bibliography and the index (which 
pertain to the whole report) have been repaginated. The title page of the Report, Jawaharlal Nehru's message, 
and Saha & Lahiri 's preface have also been included in the present volume. 

I hope that this reprinted volume will be found useful and informative by calendaric astronomers, science 
historians and scientists in general. 

S.K. Joshi 

New Delhi Director-General 

15 August 1992. Council of Scientific & Industrial Research 

and Secretary, 

Department of Scientific & Industrial Research 






Council of Scientific and Industrial Research, 
Old Mill Road, 
New Delhi. 


I am glad that the Calendar Reform Committee 
has started its labours. The Government of India 
has entrusted to it the work of examining the 
different calendars followed in this country and to 
submit proposals to the Government for an accurate 
and uniform calendar based on a scientific study 
for the t^hole of India. I am told that we have at 
present thirty different calendars, differing from 
each other in various ways, including the methods 
of time reckoning. These calendars are the natural 
result of our past political and cultural history 
and partly represent past political* divisions in 
the country. Now that we have attained independence, 
it is obviously desirable that there should be a 
certain uniformity in the calendar for our civic, 
social and other purposes and that this should be 
based on a scisntific approach to this problem. 

It is true that for governmental and many 
other public purposes we follow the Gregorian 
calendar, which is used in the greater part of the 
world. The mere fact that it is largely used, makes 
it important. It has many virtues, but even this 
has certain defects which make it unsatisfactory 
for universal use. 

It is always difficult to change a calendar 
to which people are used, because it affects social 
practices. But the attempt has to be made even though 
it may not be as complete as desired. In any event, 
the present confusion in our own calendars in India 
ought to be removed. 

I hope that our Scientists will give a lead 
in this matter. 

New Delhi, 
February 18, 1953. 




M. N. Saha, D. Sc., F. R. S., M, P., 

Director, Institute of Nuclear Physics, 
92, Upper Circular Road, Calcutta-9. 



A. C. Banerji, M. A M M. Sc., F. N. I., 

Vice-Chancellor, Allahabad University, 

Dr. K. L. Daftari, B. A., B. L M D. Litt., 

Mahal, Nagpur. 

Shri J. S. Karandikar, B. A., LL. B., 

Ex -Editor, The Kesari, 
568 Narayan Peth, 

Dr. Gorakh Prasad, D. Sc., 

Reader in Mathematics, Allahabad University, 
Beli Avenue, Allahabad, 

Prof. R. V. Vaidya, M. A., B. T M 

Senior Lecturer in Mathematics, Madhav College, Ujjain, 
78, Ganesh Bhuvan, Freegunj, Ujjain. 

Shri N. C. Lahiri, M. A., 

55A, Raja Dinendra Street, Calcutta-6. 

Shri N. C. Lahiri acted as the Secretary of the Committee. 


The scheme of transliteration of Sanskrit alphabets into Roman script adopted in this publication is the 
same as generally followed. The corresponding scripts are given below : — 




















N* B. Diacritical marks have not generally been used in names of persons belonging to recent times 
as well as in well-known geographical names. 


The Calendar Reform Committee was appointed 
in November, 1952, by the Council of Scientific and 
Industrial Research (of the Government of India) with 
the following terms of reference : 

"To examine all the existing calendars which are fceing 
followed in the country at present and after a scientific 
study of the subject, submit proposals for an accurate and 
uniform calendar for the whole of India". 

In accordance with its terms of reference, the 
Committee (for personnel, see p. 4) has scientifically 
examined all the calendars prevalent in India (vide 
Part C, Chap. V), viz*, — 

Gregorian Calendar*.. which is used for civil and 
administrative purposes (vide 
p. 170) all over the world. 

Islamic Calendar used for fixing up the dates 

of Islamic festivals (vide 
p. 179). 

Indian Calendars 

or Pancangas used for fixing up dates and 

moments of Hindu, Bauddha 
and Jaina festivals in different 
States of India* and in many 
cases for civil purposes also. 
They are about 30 in number. 
(vide Chap. V, p. 258). 
It has been pointed out (p. 171) that the Gregorian 
calendar, which is used all over the world for civil 
and administrative purposes, is a very unscientific and 
inconvenient one. The World Calendar (p* 173), 
proposed by the World Calendar Association of New 
York, has been examined and found suitable for 
modern life. The proposal for its adoption by all the 
countries of the world for civil and administrative 
purposes was sponsored by the Indian Government 
before the U. N. O. and debated before the ECOSOC 
(Economic and Social Council) at Geneva in June, 
1954 (p. 173) and its recommendations have been 
transmitted to the Governments of the World for 
their opinion. It is hoped that the World Calendar 
will be ultimately adopted. It will lead to a great 
simplification of modern life. 

The introduction of the World Calendar in place 
of the Gregorian is a matter for the whole world, 
which has now to look for decision by the U, N. O. 

The Islamic (Hejira) calendar has been discussed 
on p, 179, along with some proposals for reform 

suggested by Dr. Hashim Amir Ali of the Osmania 
University, and Janab Mohammed Ajmal Khan of the 
Ministry of Education. It is for the Islamic world to 
give its verdict on these suggestions. If these sugges- 
tions are accepted, the Islamic calendar would fall in 
line with other luni-solar calendars. 

As these two important systems of calendars had 
to be left out, the Committee's labours were confined 
to an examination of the different systems of calendars 
used by Hindus, Bauddhas and Jainas in the different 
states of India, chiefly for the fixing up of the dates 
and moments of their religious festivals, and for 
certain civil purposes as well. 

For the purpose of examining all the existing 
calendars of India, as per terms of reference, an appeal 
was issued to the Paricanga (Almanac) makers for 
furnishing the Committee with three copies of their 
Pancangas. In reply to our request 60 Pancangas 
(Almanacs) were received from different parts of the 
country and were examined (p. 21). To facilitate 
examination of the calendars, a questionnaire was 
issued to which 51 replies were received (pp. 23-31). 
In addition to the above, 48 persons offered their 
suggestions (pp. 32-38) for reform of the Indian 
calendar. These views were very divergent in 
character. Some quoted ancient scriptures to prove 
that the earth is flat, with a golden mountain in the 
centre round which move the sun and the planets, 
others tried to refute the precession of equinoxes. 
All opinions were taken into consideration in arriving 
at the decisions of the Committee. 

Principles followed in fixing up the Calendar : — The 
calendar has got two distinct uses— civil and religious. 
The Indian Calendars are used not only for fixing up 
the dates and moments of religious observances but 
also for the purpose of dating of documents and for 
certain civil purposes not only by the rural, but also 
by a large section of the urban population. There is 
great divergence in practice in different parts of the 
country in this respect. Therefore a unified solar 
calendar has been proposed for all-India use for civil 
purposes. This has been based on the correct length 
of the year (viz. the tropical year) and the popular 
month-names, vix. % Caitra, Vaisakha, etc. have been 
retained (see p. 6). 

Calendars are based partly on SCIENCE which 
nobody is permitted to violate and partly on 
CONVENTIONS which are man-made and vary from 



place to place. The Indian calendars put up by 
almanac-makers commit the violation of the following 
principles of science : — 

They take the length of the year to be 365.258756 
days (p. 240, Part C of Report) as given by the Surya~ 
Biddhdnta about 500 A. D. ; while the correct length 
of the tropical year, which alone can be used according 
to the Surya-SiddJ&nta and modern astronomy for 
calendarical use, is 365.242196 days. The difference 
of .01656 days is partly due to errors of observation, 
not infrequent in those days, and to their failure to 
recognize the precession of equinoxes. As the Surya- 
Siddhanta value of the year-length is still used in 
almanac-making, the year-beginning is advancing by 
.01656 days per year, so that in the course of nearly 
1400 years, the year-beginning has advanced by 23.2 
days, with the result that the- -Indian solar year, 
instead of starting on the day following the vernal 
equinox, i.e., on March 22, as prescribed in the Surya- 
Siddhanta (see Chap. V, p. 239), starts on April 13 or 
14. The situation is the same as happened in Europe 
due to the acceptance of 365.25 days as the length of 
the year at the time of Julius Caesar ; the Christmas 
originally linked to the winter solstice preceded it 
by 10 days by 1582 A.D., when the error was 
rectified by the promulgation of a bull by Pope 
Gregory XIII. By this, Friday, October 5 was 
proclaimed as Friday, October 15, and new leap-year 
rules were introduced. 

Unlike Europe, where the Pope in the medieval 
times possessed an authority which every one in 
Catholic Europe respected, India had a multiplicity 
of eras and year^beginnings due to her history during 
the years 500-1200 A. D. But for calendaric calcula- 
tions, our astronomers all over India have been using 
only the Saka era since Aryabhata (500 A.D.) certainly 
and probably from much earlier times, and in local 
almanacs other eras are simply imposed on it. The 
Calendar Committee has therefore recommended : — 

That for all official purposes, the Central as well 
as State Governments should use the Saka era along 
with the civil calendar proposed by the Committee 
(p.6). -It is suggested that the change-over may take 
place from the Saka year 1878, Caitra 1 (1956, March 
21}. If this is accepted, the last month of the year, viz. % 
1877 Saka, the solar Phalguna, which has a normal 
length of 30 days, will have an extra number of 6 or 
7 days. - 

The pre-eminence of the Saka era is due, as 
historical evidences cited on pp. 228-238 and 255-257 
show, that it was the earliest era introduced in India, 
by Saka ruling powers, and have been used exclusively 
by the Sakadvlpi Brahmins (forming the astrologer 
■caste) for calendar-making on the basis of Siddhantic 

(scientific) astronomy evolved by Indian astronomers 
on the basis of old Indian calendaric conceptions, 
which were put on scientific basis by blending with 
them astronomical conceptions prevalent in the West, 
from the third century B.C. 

The era is also used exclusively for horoscope 
making, a practice introduced into India since the 
first century A.D. by the Sakadvlpi Brahmanas. 

The Calendar Committee has devised a solar 
calendar with fixed lengths of months for all-India use, 
in which it has been proposed to give, up the 
calculations of the Surya-Siddhanta in which the 
solar months vary from 29 to 32 days. 

Religious Calendar — The Committee's task resolved 
itself into a critical examination of the different 
Indian local calendars, about 30 in number, which 
use different methods of calculation. This produces 
great confusion. 

As already stated the Surya-Siddhanta year being 
longer than the tropical year by about 24 mins., the 
Hindu calendar months have gone out of the seasons 
to which they conformed when the Siddhantic rules 
were framed ; as a result, the religious festivals are 
being observed not in the seasons for which they were 
intended but in wron* seasons. The Committee felt 
that the error should be corrected once for all and 
the months brought back to their original seasons. 
But with a view to avoiding any violent break in the 
present day practices, the desired shifting has not 
been effected, but any further increase of the error has 
been stopped by adopting the tropical year for our 
religious calendar also (sec p. 7). 

Before the rise of Siddhanta Jyotisa ( 400 A.D. ), 
India used only the lunar calendar calculated according 
to the Vcdahga Jyotifa rules and most religious festi- 
vals ( e.g. the Janm3ftami, the birthday of Sri Krsna ) 
used to be fixed up by the lunar calendar which used 
only t i tli i and naksatra. The Calendar Committee 
could not find out any way of breaking off with the 
lunar affiliation short of a religious revolution and 
has, therefore, decided to keep them. For this 
purpose, the lunar year is to be pegged on to the solar 
year by a number of conventions. The Committee has 
adhered to the ancient conventions as far as possible. 
But the erroneous calculations of tithis and naksatras 
have been replaced by modern calculations given in 
the nautical almanacs and modern ephemcrides, and 
the religious holidays have been fixed for a central 
station of India ( tide page 40 ). 

The present practice is to calculate the tithi for 
each locality and the result is that the same tithi 
may not occur on the same day at all places. The 
Calendar Committee has found that the continuance 


of different lunar calendars for different places is a 
relic of medieval practice when communication was 
difficult, the printing press did not exist and 
astrologers of each locality used to calculate the 
calendar for that locality based on Siddhantic rules 
and used to proclaim it on the first day of the year 
to their clients. In these days of improved communi- 
cation, free press, and radio, there is not the slightest 
justification for continuance of this practice and the 
Committee has fixed up the holidays for the central 
station (82° 30' E, 23° 11' N, see Report p. 40); 
and recommended that these holidays may be used for 
the whole of India. The dates of festivals of the 
Hindus, Jainas and Bauddhas have been determined on 
the above basis. This will put an end to the calendar 

The confusion is symbolic of India's history. 
While all Christendom comprising people of Europe, 
Asia and America, follows the Gregorian calendar, 
and the whole of the Islamic world follows the Hejira 
calendar for civil and religious purposes, India uses 30 
different systems for fixing up the same holidays in 
different parts of the country and frequently, two 
rival schools of pancanga-makers in the same city fix 
up different dates for the same festival. This is a 
state of affairs which Independent India cannot 
tolerate. A revised national calendar, as proposed 
by us, should usher a new element of unity in 

The Committee has therefore gone deeply into the 
history of calendar making in all countries from the 
earliest times particularly into the history of calendar- 
making in India (vide Chap. V) and has arrived at their 
conclusions. Its recommendations are entirely in 
agreement with the precepts laid down by the Siddhan- 
tic astronomers, as given in the Stirya-Siddhanta and 
other standard treatises (see p. 238 et seq.). 

The Committee has also compiled a list of all reli- 
gious festivals observed in diffirent parts of India and 
listed them under the headings (i) Lunar, and (ii) Solar, 
with their criteria for fixing the dates of their obser- 
vances (pp. 102-106). 

Where does the Government come in : Though India 
is a secular state, the Central Government and the 
State Governments have to declare a number of holi- 
days in advance, a list of which. will be found on pages 
117-154 for the Central Government as well as for the 
States. These holidays are of four different kinds, 
viz. : — 

(i) Holidays given according to the Gregorian 
calendar,,, Mahaima Gandhi's birthday, 
which falls on Oct. 2. These present no 
problem to any government. 


(ii) But there are other holidays, which are given 
according to the position of the Sun (vide 
pp. 117-118). 

(iii) Others which are given according to thb luni- 
solar calendar (pp. 119-124). 

(iv) Holidays for Moslems and Christians (pp. 125 
and 126). 

* It is a task for the Central as well as State Govern- 
ments to calculate in advance dates for the holidays it 
gives. This is done on the advice of Pancanga-makers 
attached to each Government. In addition, numerous 
indigenous pancangas arc prepared on the Siddhantic 
system of calculations, the elements of which arc now 
found to be completely erroneous. There is a wide 
movement in the country first sponsored by the 
great savant, patriot and political leader, the late 
Lokamanya B. G. Tilak, for making the pancaiiga 
calculations x>n the basis of the correct and up-to 
date astronomical elements. As a result, there are 
almost in every State different schools of pancariga 
calculations, differing in the durations of tithis, 
naksatras, etc., and consequently in the dates of 
religious festivals. The problem before the Govern- 
ment is : which one of the divergent systems is to be 
adopted. The Committee has suggested a system of 
calculations for the religious calendar also, based on 
most up-to-date elements of the motion of the sun and 
the moon. Calendars for five years from 1954-55 to 
1958-59 have been prepared on this basis showing 
therein inter alia the dates of important festivals of 
different States (vide pp. 41-100). The lists of holidays 
for the Government of India and of each separate 
State for the five years have also been prepared from 
this calendar for the use of the Governments. The 
Committee hopes that the Government of India as well 
as the State Governments would adopt these lists in 
declaring their holidays in future. The Ephcmerides 
Committee which has been formed by the Government 
pi India, consisting of 'astronomers versed in the 
principles of calendar-making would act as advisers to 
the Central as well as State Governments. It may be 
assisted by an advisory committee to help it in its 

The responsibility of preparation of the five-yearly 
calendar and the list of holidays on the basis of 
recommendations adopted by the Committee has been 
shared by Sri N. C. Lahiri and Sri R. V. Vaidya, 
aided by some assistants and several pandits of notjc, 
amongst whom the following may be mentioned : 
Sri A. K. Lahiri, Sri N. R. Choudhury, Pandit 
Narendranath Jyotiratna, and Joytish Siddhanta 
Kesari Venkata.Subba Sastry of Madras. 

We have received great help from C. G. Rajan, 
B.A., Sowcarpet, Madras. He has kindly furnished 


us with valuable suggestions regarding 'Rules for 
fixing the dates of festivals for South India*. 

We are indebted to the Astronomer Royal of Great 
Britain, Sir Harold Spencer Jones, and to Mr. Sadler, 
head of the Ephemcrides divison of the Royal 
Observatory of U. K. for having very kindly supplied 
us with certain advance data relating to the sun and 
the moon which have facilitated our calculations. We 
have to thank the great oriental scholar, Otto Ncuge- 
bauer for having helped us in clearing many obscure 
points in ancient calcndaric astronomy. We wish to 
express our thanks to Prof. P. C. Scngupta for helping 
us in clearing many points of ancient and medieval 
Indian astronomy. 

We have reproduced figures from certain books 
and our acknowledgement is due to the publishers. It 
was however not possible to obtain previous permission 
from them, but the sources have been mentioned at 
the relevant places. 

It is a great pleasure and privilege to express our 
gratitude to our colleagues of the Calendar Committee 
for their active co-operation in the deliberations of the 
Committee, and ungrudging help whenever it was 
sought for. 

M. N. Saha 
Calcutta, Chairman 
The 10th Nov., 1955. N. C. Lahiri 






History of the Calendar in different 
Countries through the Ages 


Prof. M. N. SAHA, d. sc., f. r. s. 

Professor Emeritus, University of Calcutta, 
Chairman, Calendar Reform Committee, 


Sri N. C. LAHIRI, m. a. 

Secretary, Calendar Reform Committee. 



History of the Calendar in different countries through the ages 





I — General Principles of Calendar Making 



The Zodiac and the Signs 



... 157 


Chaldean contributions to astronomy: 


The natural periods of time 

Rise of planetary and horoscopic 



The problems of the Calendar 

... 158 


Greek contributions to astronomy 


Subdivisions of the day 

... 159 


Discovery of the precession of the 


Ahargana or heap of days: Julian days 

... 161 


11— The Solar Calendar 




Time reckonings in ancient Egypt 

... 164 


—Newton's explanation of the precession 


Solar calendars of other ancient nations 

... 165 

of the equinoxes 


The Iranian Calendar 

... 166 

4-B — Stars of the lunar mansions 


The French Revolution Calendar 

... 167 


The Roman Calendar 

... 168 

V — Indian Calendar 


The Gregorian Calendar 

... 170 


The periods in Indian history 


The World Calendar 

... 171 


Calendar in the Rg-Vedic age 


Calendaric references in the 

III — The Luni-Solar and Lunar Calendars 


Yaj ur- Vedi c 1 i terature 


Principles of Luni -solar calendars 



The Vedanga Jyotisa Calendar 


Moon's synodic period or lunation: 


Critical review of the inscriptional 

Empirical relation between the year and 

records about calendar 

the month 

... 175 


Solar Calendar in the Siddhanta Jyotisa 


The Luni-solar calendars of the 


Babylonians the Macedonians, the 


Lunar Calendar in the Siddhanta Jyotisa 

Romans and the Jews 

... 176 



The introduction of the era 

... 177 


Indian Eras 


The Jewish Calendar 

... 179 


The Islamic Calendar • 

... 179 



— The Seasons 

IV — Calendaric Astronomy 



— The Zero-point of the Hindu Zodiac 


The Moon's movement in the sky 

... 181 


— Gnomon measurements in the Aitareya 


Long period observations of the moon: 


The Chaldean Saros 

... 184 


— Precession of the Equinoxes amongst 


The Gnomon 

... 188 

Indian Astronomers 


Night observations: the celestial pole 


— The Jovian years 

and the equator 

... 190 


The apparent path of the sun in the sky: 


The Ecliptic 

... 191 





... 207 
... 210 






. 259 

.. 266 

.. 270 

. 271 
. 273 





















A C 













H E M E N i D 











— f 1" 

E M P / RE 







Asia minor 







































First • 


Third • 
Fourth . 


positions or the: first point or 


V = VeJic Times ahoul 2300 B.C. 
/f = Hipparchoj UO B.C. 

PiU Ptolemy 150 A.D. 

Sj - Surya SicJdhan/a 2.85 A.D. 

S 2 « , 500 A.D. 

Sj =r 510 AD. 

M = Modern 1950 A.D. 


General Principles 


The Flux of Time, of which we are all conscious, is 
apparently without beginning or end, but it is cut up 
periodically by several natural phenomena, vix. : 

(1) by the ever-recurring alternation of daylight 
and night, 

(2) by the recurrence of the moon's phases, 

(3) by the recurrence of seasons. 

If is these recurring phenomena which are used to 
measure time. 

These phenomena have the greatest importance for 
man, for they determine all human and animal life. 
Even prehistoric men could not help noticing these 
time-periods, and their effect on life. 

When human communities started organized social 
life in the valleys of the Indus and the Ganges (India), 
the Nile (Egypt), the Tigris and the Euphrates 
(Mesopotamia) and the Hoang Ho (China), several 
millenia before Christ (vide Chronological Table), these 
phenomena acquired new importance. For these early 
societies were founded on agriculture ; and agricultural 
practices depend on seasonal weather conditions. 
With these practices, therefore, grew national and 
religious festivals, necessary for the growth of social 
life, and of civilization. People wanted to know in 
advance when to expect the new moon or the full moon, 
when most of the ancient festivals were celebrated ; 
when to expect the onset of the winter or the 
monsoon ; when to prepare the ground for sowing ; 
the proper time for sowing and for harvesting. 
Calendars are nothing but predictions of these events, 
and were early framed on the basis of past experiences. 


The three events mentioned in (1), (2) and (3) above 
define the natural divisions of time. They are : 

The Day : defined by the alternation of daylight 
and night. 

The Month : the complete cycle of moon's changes 
of phase, from end of new-moon to next end of new- 
moon (amdnta months), or end of full-moon to end 
of next full-moon {purnimUnta months). 

The Year : and its smaller subdivisions, viz., the 

: Calendar Making 

The Day* : 

The day, being the smallest unit, has been taken as 
the fundamental unit of time and the lengths of months, 
the year and the seasons are expressed in terms of the 
day as the unit. 

But the day is to be defined. Many early nations 
defined the day as the time-period between sunrise 
to sunrise (savana day in India) or sunset to sunset 
(Babylonians and Jews). But the length of the day, 
so defined, when measured with even the rough 
chronometers of early days, was found to be variable. 
This is due to the fact that except at the equator, the 
sun does not rise or set at the same time in different 
seasons of the year. So gradually the practice arose 
of defining the day as the period from midnight to 
midnight, i. e., when the sun is at the nadir to its next 
passage through the nadir. Even then the length of 
the day is found to be variable when measured by an 
accurate chronometer. The reasons are set forth in all 
astronomical text books. Then came the idea of the 
mean solar day, and it is now taken as the funda- 
mental unit of time. The mean solar day is -the 
average interval between the two successive passages 
of the sun over the meridian of a place derived from a 
very large number of observations of such meridian 
passages. The time between two passages is measured 
by an accurate chronometer. 

In addition to the solar day, the astronomers define 
also a sidereal day, which is the time period between 
two successive transits of a fixed star. It measures 
the time of rotation of the earth round its axis.t 

The solar day is larger than the sidereal day, 
because by the time the earth completes a rotation 
about its axis, the sun slips nearly a degree to the east, 
due to the motion of the earth in its orbit, and it 
takes a little more time for the sun to come to the 

* Day here means 'Day and Night'. In ancient times, the 
duration of day-light from sunrise to sunset, and of : the night from 
sunset to sunrise, were measured separately with the aid of water- 
clocks. It was comparatively late that the length of the Day, meaning 
day-light and night, was measured. It was distinguished by the term 
ahoratra in Sanskrit, ahna meaning daylight time, and rain meaning 
night time. In Greece, this was known as Nychthemeron. 

+ Actually speaking, the sidereal day is defined in astronomy as 
the period between two successive meridian passages of the First 
point of Aries. As this point has a slow westward motion among 
the fixed stars, the duration of the so called sidereal day is very 
slightly less than the actual sidereal day or the period of rotation of 
the earth. 



meridian of the place. We have the relation : 
365J mean solar days«366J sidereal days. 
Rotation of the earth =23 b 56™ 4M00 mean solar time. 
Sidereal day = 23 56 4.091 „ » » 

Mean solar day =24 3 56.555 sidereal time 

The actual sidereal day, which measures the period 
of rotation of the earth is generally taken to be cons- 
tant. The variable part of the solar day comes from 
two factors : 

(1) Obliquity of the sun's path to the equator, 

(2) Unequal motion of the sun in different parts 
of the year. 

(See H. Spencer Jones, General Astronomy p. 45). 
It has however been recently found that even the 
period of rotation of the earth is not constant but 
fluctuates both regularly and irregularly by amounts 
of the order of 10- • seconds. & 

The Month : 

The month is essentially a lunar phenomenon, and 
is the time-period from completion of new moon 
{conjunction of moon with the sun) to the next new 
moon. But the length of the month so defined varies 
from 29.246 to 29.817 days, owing to the eccentricity 
of the moon's orbit and other causes. The month or 
lunation used in astronomy is the mean synodic 
period, which is the number of days comprised within 
a large number of lunations divided by the number of 
lunations. Its value is given by 

1 lunation = 29. d 5305882— O. d 0000002 T 
where T = no. of centuries after 1900 A.D. 

The present duration of a lunation *= 29*5305881 
days or 29 d 12 h 44 m 2. s 8. There are other kinds of 
months derived from the moon and the sun which 
will be discussed later. 

The Year and the Seasons : 

The year is the period taken by the seasonal 
characteristics to recur. The early people had but a 
vague notion, of the length of the year in terms of 
the day. In the earliest mythology of most nations, 
the year was taken to have comprised 360 days, consis- 
ting of 12 months each of 30 days. They apparently 
thought that the moon's phases recur at intervals of 
30 days. 

But experience soon showed that these measures 
of the month and the year were wrong, but they have 
left their stamp on history. The sexagesimal measure 
used in astronomy and trigonometry, as well as fanci- 
ful cycles of life of the Universe, invented by ancient 
nations, appear to have been inspired by these 

It appears that the Egyptians found very early 
(as related in the next section) from the recurrence 
of the Nile floods that the year had a length of 365 
days. Later they found the true length to be nearer 
365.25 days. 

The ancient Babylonians, or Chaldeans as they 
were called from about 600 B.C., appear to have been 
the earliest people who tried to obtain correct 
measures of the time-periods ; the month, the year, 
and the seasons in terms of the day, and its subdivi- 
sions. Their determinations were transmitted to 
the Greeks who refined both the notions and measure- 
ments very greatly. This story will be told in 
Chapter II. 

At present it is known that the length df the 
seasonal year (tropical year) is given by :— 

Tropical year = 365-24219879— '0*614 (t— 1900) days, 
where t= Gregorian year. 

The present duration of a tropical year is 
365*2421955 days or 365 d 5 h 48 m 45-7. 

The Sidereal Year : 

In some countries, the ancients took the year to 
be the period when the sun returned to the same 
point in its path (the ecliptic). This is the time of 
revolution of the earth in its orbit round the sun. 
The tropical year, or the year of seasons, is the time 
of passage of the sun from one vernal equinox 
to the next vernal equinox. The two years would 
have been the same, if the vernal equinoctial point 
(hereafter called the vernal point) were fixed. But 
as narrated in Chapter IV, it recedes to the west at 
the rate of 50" per year. The tropical year is there- 
fore less than the sidereal year by the time taken by 
the sun to traverse 50% i.e., by .014167 days or 
20 m 24 s . 

For calendarical purpose, it is unmeaning to use 
the sidereal year (365 d . 256362), as then the dates 
would not correspond to seasons. The use of the 
tropical year is enjoined by the Hindu astronomical 
treatises like the Surya Siddhanta and the PaMca 
Siddhantika. But these passages have been misunder- 
stood, and Indian calendar makers have been using 
the sidereal year with a somewhat wrong length 
since the fifth century A.D. 


Whatever may be the correct lengths of the astro- 
nomical month and the year, for application to human 
life, the following points have to be observed in 
framing a civil calendar. 

(a) The civil year and the month must have an 
integral number of days. 



(b) The starting day of the year, and of the month 
should be suitably defined. The dates must correspond 
strictly to seasons. 

(c) For purposes of continuous dating, an era 
should be used, and it should be properly defined. 

(d) The civil day, as distinguished from the 
astronomical day, should be defined for use in the 

(e) If the lunar months have to be kept, there 
should be convenient devices for luni-solar adjustment. 

A correct and satisfactory solution of these pro- 
blems has not yet been obtained, though in the form 
of hundreds of calendars which have been used by 
different people of the world during historical times, 
we have so many attempted solutions. The early 
calendars were based on insufficient knowledge of the 
duration of the natural time cycles— day, month and 
year — an ^ l e( l to gross deviations from actual facts, 
which had to be rectified from time to time by the 
intervention of dictators like Julius Caesar, Pope 
Gregory XIII, or a founder of religion like Mohammed, 
or by great monarchs like Melik Shah the Seljuk, or 
Akber, the great Indian emperor. 

Owing to the historical order of development, 
calendars have been used for the double purpose : 

(i) of the adjustment of the civic and adminis- 
trative life of the nation, 

(ii) of the regulation of socio-religious life of the 

In ancient and medieval times, society, state and 
church were intermingled, and the same calendar 
served all purposes. The modern tendency is to 
dissociate civic life and administration from socio- 
religious life. Also due to the enormous growth of 
intercourse amongst all nations of the world, the need 
has been felt for a World Calendar dissociated from 
all religious and social bias. Owing to historical 
reasons, the Gregorian calendar is now used inter- 
nationally for civic and administrative purposes, but 
it is very inconvenient, and proposals have been made 
to the U. N. O. for the adoption of a simple World 
Calendar (vide § 2.7). 


For pactical prurposes, the day is divided into 24 
hours, an hour into sixty minutes and a minute into 
sixty seconds. 

1 mean solar day « 24 x 60 x 60 = 86, 400 seconds. 

The subdivisions of time are measured by highly 
developed mechanical contrivances (clocks, watches 
and chronometers), but they have come into use only 

during comparatively recent times. The ancient people 
used very primitive devices. 

The time-keeping apparatus of the ancients were 
the gnomon, the sundial, and the water-clock or the 
clepsydra. The first two depend on the motion of the 
sun, and require correction. The water-clock which 
probably was first invented in Egypt, appears to have 
been used down to the time of Galileo, when the 
discovery of pendulum motion 1 led to the invention of 
clocks based on pendulum motion or use of the balance 

Subdivisions of time can be measured by the motion 
of any substance, which repeats itself regularly ; at the 
present time in addition to pendulum clocks, quartz- 
clocks, and ammonia clocks have been used. The 
latter depend upon harmonic motions within the 
ammonium molecule, giving rise to spectral lines whose 
frequency can fcfe accurately measured. 

The present divisions of the solar day have 
interesting history. 

It is stated by Sarton that the ancient Sumerians 
(original dwellers of Babylon) divided the day-time and 
night-time into three watches each. The watches 
were naturally of unequal lengths and varied through- 
out the year. It was only during equinoxes that the 
watches were of equal length, each of our 4 hours. 

These unequal watches continued down to medieval 
times. The life of a medieval monk was watch-wise as 

(1) Matins— last watch of the night. The monk 

got up nearly two hours before sun- 
rise and started his work, 

(2) Prima— at sunrise, 

(3) Tertia — half-way between sunrise and noon- 

time of saying Mass, 

(4) Sexta— at noon (hence the word, Siesta- 

midday rest), 

(5) Nona— mid-afternoon, whence our word Noon, 

(6) Vespers— an hour before sunset, 

(7) Compline— at sunset. 

The watches were variable in duration and in their 
starting moments. Sarton remaks : 

A clock regularly running and dividing the day into 
periods of equal duration would have been, at first, more 
disturbing than useful. For monastic purposes, a human 
variable clock {e. g. a bell rung by a monk or lay brother 
at the needed irregular intervals) was more practical than 
an automatic one.* 

But even in ancient times, the need for measure- 
ment of equal intervals of time was felt. The ancient 
Babylonians used the Nychthemeron (Day and Night 

*Sarton, Introduction to the History of Science, Vol. Ill, Part I, 
p. 716. 


combined- JMrafro) into 12 hours of 30 Qesh each, 
Qesh being -4 minutes. The Egyptians divided the day- 
light time into 12 hours, and the night into 12 hours. 
Later in medieval times, the 24-hour division for the 
whole day (day and night) has been adopted. The 
division into A.M. and P.M. were for the sake of 
convenience, so that the maximum number of times a 
bell has to be rung, on the completion of an hour, 
would not exceed 12, for apparently ringing a bell 24 
times would be a torture of the flesh. 

The broad divisions of the day were secured by the 
Hindus in two ways. They divided the day-time (from 
sunrise to sunset) into 4 equal parts each called a 
prahara or yama. The night time was also similarly 
divided into 4 equal praharas. The prahara is so 
popular a unit in Indian time measurement that even 
the lay man expresses time in terms of praharas and 
half praharas. An alternative system of division of the 
time is the 'muhurta' obtained by dividing the daytime 
into 15 muhurtas determined by gnomon shadow 
lengths The day muhurtas were measured from 
lengths of shadows of the gnomon. The night muhurtas 
ate similarly the fifteenth part of the night time. 

As the durations of day and night are not equal 
except on the vernal and autumnal equinox days, the 
Prahara and muhurta of the day-time have not the 
same durations as those of their nocturnal counterparts. 
On equinox days, they are however equal, when 

1 Prahara =3* <P-7* 30- 
1 Muhurta =0 48 =2 
The Hindu astronomers appear to have switched on 
to the ahoratra during Vedariga Jyotisa times. As it is 
rather complicated, we do not give an account of it. 
The reader may consult Dixit's Bharatiya Jyohsastra. 
But in Siddhanta Jyotisa, they had a full fledged 
scientific system. 

The scientific divisions of time followed by the 
Siddhantas are the ghatika {davda or nadil prahara or 
yama. and muhurta etc. The day is measured from 
sunrise and the period from sunrise to next sunrise is 
divided into 60 equal 'ghatika^ °* dan^as ; each ghatx 
is subdivided into 60 vighatis or palas. and each mghaix 
or pala into 60 vipalas. So a day consists of 60 >ghatis 
or 3600 palas or 216000 vipalas. Thus 
1 ghatika -24 m 0*.0 
I pala - 24.0 
1 vipala = 0.4 

The pala or vighati is sometimes subdivided into 6 
divisions called a prana. A prana is therefore equi- 
valent to 4 sees, of time. There are 360 pranas in a 
ghatjka and the day contains 360 x 60 or 21600 pranas, 


the same as the number of minutes ( kola or lipiika ) in 
a circle. In Siddhantas (astronomical treatises of the 
Hindus) there are conceptions with nomenclatures of 
still smaller divisions of time, but they had no practi- 
cal utility. 

None of the time-periods of the sun, and the moon, 
m%. the year and the season, and the lunations and 
half-lunations are integral multiples of the day ; on the 
other hand, the figures run to several places of 
decimals. How did the ancients, who quickly dis- 
covered that the time-periods were not integral multi- 
ples of the day, express their findings ? 

It will take us a long dive into the history of 
mathematical notation to elucidate this story. The 
curious reader may consult Neugebauer's Exact Sciences 
in Antiquity or van der Waerden's Science Awakening 
(pp 51-61). In fact, the symbolism was very cumbrous 
before the discovery of the decimal notation about 
600 A.D. in India, where it quickly replaced the old 
cumbrous notation. The discovery was quickly adopted 
by the Arabs for certain purposes, but was first made 
known to Europe by Leonardo of Pisa in a treatise on 
Arithmetic published in 1202 A.D., but a few more 
centuries passed before it was universally adopted. 

The practice of expressing fractions by means of 
decimals came later, both in India and Europe. In 
India an astronomer who wrote an astronomical 
treatise called 'Bhasvati* in 1099 A. D. was called 
Satananda, (i.e. revelling in hundreds) because he 
used to write fractions in hundredths i.e. i as 25 
hundredths, f as 75 hundredths. In Europe, the 
expression of fractions by decimals came into vogue 
about the seventeenth century. 

The Hindu astronomer of the Siddhantic age 
expressed the periods of the sun, the moon and the 
planets by the number of their periods in a Mahayuga 
(4.32 x 10 6 years). The number is usually integral. 
But how did this cumbrous system originate ? 
Probably many of these values were obtained by 
counting the number of days between a large number 
of periods and dividing them by the number of periods. 
For example, take the case of the length of the mean 
lunation (lunar month). All ancient nations give 
this length correct to a large number of decimals. This 
must have been obtained by counting the number of 
days between two new moons, separated by a large 
number of years, and dividing it by the number of 
lunations contained in the interval. Of course, the 
utmost they could have done was to keep records for 
at most a hundred years, but the rule of three was 
always available. 

In the following sections, the different ways of 
tackling the calendar problem in different centres of 



civilization have been described. We have described 
in Chap. II, the purely solar calendars, in which the 
moon is altogether discarded as a time-marker. This 
practice originated in Egypt about 3000 B.C. These 
calendars require only a correct knowledge of the 
length of year, and are therefore comparatively simpler. 
They required very little or almost no knowledge 
of astronomy. 

We have described in Chap. Ill, the luni-solar 
calendars, prevalent in ancient Mesopotamia, India, 
China and most other countries. In these calendars, 
both the sun and the moon are used as time-markers, 
and therefore precise knowledge of their motion in 
the heavens was essential for the formulation of a 
correct calendar. We mark two stages : first the 
formulation of a calendar from a knowledge of only 
the length of the year, and of the mean lunar 
month. This was an older phase. It did not work 
satisfactorily, because it depended on the mean motion 
of the two luminaries. Actually, the time-predictions 
have to be verified by actual comparison of the 
predicted happenings (say of the vernal equinox 
day in the case of the sun, or the first appearance 
Of the crescent of the moon after new moon on the 
western horizon) with the time of actual happenings. 
This gave rise to the need for watching the daily 
motion of the two luminaries, and invention of 
methods for recording and storing these observations ; 
in other words/ this led to the science of astronomy. 
Early astronomy is almost completely calendarical. 
At a later stage, the five planets attracted attention, 
on account of their association with astrology. 

We have therefore devoted Chap. IV to calendaric 
astronomy, which was evolved by the Chaldeans and 
taken over from them by the Greeks, and in time 
diffused to other countries. 

In Chap. V, we have described the various stages of 
the development of the Indian calendar : — the empiri- 
cal stage (Rg-Vedic), the mean motion stage ( Vedanga 
Jyoti$a), and the scientific stsfge (Siddhanta Jyoti$a). 
From 1200 A.D., astronomical studies became decadent 
in India, and we have analysed the cause of decadence. 
We have given a full account of precession, as most 
Indian calendar makers still believe in the false theory 
of Trepidation which disappeared from Europe after 
1687 A. D. 


Though the Flux of Time is a continuous process, 
it is divided for the sake of convenience and for 
natural reasons too, into years, months and days. 
The years are mostly counted from the beginning of 
an era, so that if we wish to date a memorable event, 

say the birth-day of George Washington, it can be 
seen from an inspection of his birth register that it 
took place on Feb.ll, of the year 1732. But this 
practice by itself does not enable a scientific chrono- 
logist to fix up the event unambiguously on the 
absolute Scale of Time, unless the whole history of 
the particular method of date-recording is completely 
and accurately known One must know the lengths 
of the individual months, the leap-year rules, and 
the history of calendar reform. In the particular case 
mentioned, though George Washington * according to 
his birth register is stated to have been born on Feb. 
11, 1732, his birth-day is celebrated on Feb. 22. Why ? 
Because Feb. 11 was the date according to the Julian 
calendar. But in 1752, England (America was then 
a colony of England) adopted the reformed Gregorian 
calendar, and by an Act of Parliament, declared Sept. 
3 to be Sept. 14, a difference of 11 days. Following 
the Gregorian calendar, Washington's birth-day had 
to be shifted to Feb. 22. A scientific chronologist, say 
of China, would find it difficult to locate Washington's 
birth-day unless he knew the whole history of the 
Gregorian calendar. 

This difficulty is more pronounced when we 
have to deal a luni-solar calendar, say that of Babylon. 
Many records of lunar eclipses occuring in Babylon 
were known to the Alexandrian astronomer, Claudius 
Ptolemy, but they were dated in Seleucidean era, and 
Babylonian months, say year 179, 10th of Nisan. Now 
the Babylonian months were lunar, had lengths of 29 
or 30 days, but the year could have lengths of 353, 354 
383, 384 ( vide § 3'3 ). Therefore when two eclipse 
datings were compared, it was impossible to calculate 
the number of days between them, unless the investi- 
gator had before him a record showing the lengths of 
years and months between the two events. Ptolemy 
expressed his datings according to the Egyptian calen- 
dar, which enables one to calculate the interval far 
more easily. He must have taken lot of pains to carry 
out the conversion from the Babylonian to Egyptian 

How much better it would have been if a great 
genius at the beginning of civilization, say near about 
3000 B.C., started with a zero day, and started the 
practice of dating events by the number of days 
elapsed since this zero date, to the date when this 
particular event took place. Such a great genius did 
not appear and a confusing number of calendars came 
into existence. The scientific chronologist is now 
faced with the reverse problem : Suppose two ancient 
or medieval events are found dated according to two 
different calendars. How to reduce these dates to an 
absolute chronological scale ? 

For this purpose, a medieval French scholar, Joseph 
Scaliger introduced in 1582 A. D., a system known as 


'Julian Days' after his father, Julius Scaliger. The 

Julian period in years is 

7980 years -19x28x15 
19 being the length ia years of the Metonic Cycle, 
- c „ of the Cycle of Indiction, 

A O o , of the Solar Cycle, 

and 28 » » » n » 

It was found by calculation that these three cycles 
started together on Jan. 1, 4713 B.C. So the Julian 
period as well as the Julian day numbers started from 
that date. The Julian period is intended to include all 
dates both in the past and in the future to which refe- 
rence is likely to be made and to that extent it has an 
advantage over an era whose epoch lies within the 
limits of historical time. The years of the Julian 
period are seldom employed now, but the day of the 
Julian period is frequently used in astronomy and 
calendaric tables. Unlike the civil day, the Julian day 
number is completed at noon. 

Let us give the Julian days for a number of world- 
events, asgivenbyGinzel, in his Eandbuch der Mathe- 
matischm und Technischen Chronologic 


Saka era 
Burmese era 
Newar era 
Jelali era 

Table 1 — Julian day numbers. 

... 17 February, 3102 B.C. 
... 26 February, 747 B.C. 
... 12 November, 324 B.C. 
... 15 March, 78 A.D. 
... 29 August 284 A.D. 
... 16 July, 622 A.D. 

Julian day 

.. 588,465 

16 June, 632 A.D. 1,952,063 

21 March, 638 A.D. 1,954,167 

20 October, 879 A.D. 2,042,405 

15 March, 1079 A.D. 2,115,236 


It may be mentioned here that the ideas underlying 
continuous reckoning of days occurred much earlier to 
the celebrated Indian astronomer, Sryabhata I (476- 
525A.D.), who introduced it under the designation 
''AharganJ* or heap of days in his celebrated Arya- 
bha\\ya. The idea of counting ahar ^V^ or heaps of 
days elapsed from a specified epoch upto the given date 
dawned upon the Hindu astronomers as a necessity for 
calculating the position of planets for that date. They 
followed the cumbrous luni-solar calendar for dating 
purposes, which was not based upon any simple rules. 
It contains months of 29 or 30 days, and occasionally a 
thirteenth month, the recurrence of which was deter- 
mined by elaborate methods. The dates of the months 
are not numbered serially, but designated by the 
tithi current at sunrise. It was accordingly found 
almost impossible to work out the mean positions of 
planets on the basis of the luni-solar calendar alone. 

For this purpose a continuous and uniform time scale 
was necessary, and this was served by the ahargaQa. 

Sryabhata had somehow the idea that the planets, 
and the two nodes (which were treated as planets 
in Hindu astronomy) return to the first point of Aries 
after every 4.32 x 10 6 years, and there was a unique 
assemblage of planets at the first point of the Hindu 
sphere at some past date which he called the beginning 
of Kali Yuga. The date assigned to the Kali beginning 
is now known to be 3102 B.C., February 17-18. The 
common period of revolution of planets of 4.32 x-10 6 
years constitute a Mahayuga consiting of 

Satya yuga of 1.728 x 10° years 

Treta yuga of 1.296 x 10 6 " 

Dvapara yuga of 0.864 x 10* " 

Kali yuga of 0.432 x 10 6 " 

Total 4.32 x 10 6 years 

It may be noticed that 

4.32 xl0 c ~ 12000 x 360 

Sryabhata gave tables showing the number of 
sidereal revolutions of planets . in the period of 
4.32xl0 6 years. The total number of days in a 
Mahayuga- 1,577,917,800 which gives the length of a 
year = 365.25875 days. 

Brahmagupta was evidently not satisfied that 
Sryabhatas figures for the periods of planets were 
correct. He introduced a Kalpa = 1000 Mahayugas - 
4.32 xlO 9 years. The ' Kalpa was supposed to consti- 
tute a 'Day of the Creator, Grand-father Brahma. 
He gave the number of. sidereal revolutions of the 
planets in a Kalpa, and thought he had improved 
Sryabhatas figure for the year. 

Brahmagupta s year = 365.25844 days. 

Sryabhata calculated 'Ahargana' or heap of days, 
from the beginning of the Mahayuga as the zero-day. 

But evidently this practice involves very large 
numbers, and is inconvenient to use. Therefore the 
later astronomers used modifications of the system 
by counting Ahargaw from other convenient epochs, 
within historical reach. The different epochs which 
have been used are : — 

(1) The beginning of the Kali era or 3102 B.C. 

(2) 427 Saka era or 505 A.D. as is found in 
FaftcasiddhanUka of Varahamihira. 

(3) 587 Saka era or 665 A.D. as is found in the 
Kha^iakhUyaka of Brahmagupta. 

(4) 854 Saka era or 932 A.D, as is found in the 
Laghurn&nasa of Muiijala. 

(5) 961 Saka era or 1039 A.D. in the Siddhftnta 
Sehhara of Srlpati. 

The astronomical treatises of the Hindus have been 
divided into three categories according to the initial 



epoch employed for calculation. In which the calcula- 
tions of ahargay,a as well as the planetary mean places 
are made from the Kalpa, is called a Siddhanta ; when 
the calculations start from a Mdhayuga or Kali' 
beginning it is called a Tantra, and when it is done 
from a recent epoch it is called a Karaw. In any 
case, the mean places of the planets with their nodes 
and apsides are given for the epoch of the treatise 
from which calculations are to be started, with rules 
for finding the aharga^a for any later date. This 
ahargaya is then made use of in finding for that later 
date the positions of planets from their given initial 
positions and their daily motions, for, 

The mean position at any epoch 

= the mean position at the initial epoch 

+ daily motion x ahargana. 
Due to the complexity of the Hindu luni-solar 
calendar, one has to go through complicated rules in 
determining the ahargaria for any particular day. 
Dr. Olaf Schmidt of the Brown University and the 
Institute of Advanced Study, in discussing the method 
of computation of the Aharga<$a at length, has pointed 
out that the present Hindu method suffers from a 

disturbing discontinuity. The curious reader may go> 
through his article published in the Centaurus. 

We, however, give below the corresponding Julian 
day numbers and Kali ahargana for certain modern 

Julian days 

(elapsed at 
mean noon) 


Kali ahargaipa 
(elapsed at 
following midnight) 


1900, Jan. 1 
1947, Aug. 15 
1956, Mar. 21 

The difference between the two numbers 588,465 
represents the Julian day number on the Kali epochs 
as already stated. 

The use of ahargana plays a very important part in 
modern epigraphical researches when the date recorded 
in an inscription is required to be converted into the 
corresponding date of the Julian calendar. If the 
Kali aharga<$a for the recorded date can be determined, 
then the problem of ascertaining the corresponding. 
Julian or Gregorian date becomes a very easy task. 


The Solar 


Like other nations of antiquity the early Egyptians 
had a year of 360 days divided into 12 months, each 
of 30 days ; but they found very early from the 
recurrence of the Nile flood, that the seasonal year 
consisted approximately of 365 days, and that a month 
or lunation (period from one new-moon to another) 
was nearly 29| days (real length 29.531 days). But 
they had already framed a calendar on the 30-day 
month, and 360-day year, which had received religious 
sanction. Hence arose the first necessity for calendar- 
reform recorded in ancient history. To persuade the 
people to agree to this reform their priests invented 
the following myth : 

"The Earth god Seb and the sky goddess Nut had once 
illicit union. The supreme god Ra, the Sun, thereupon 
cursed the sky goddess Nut that the children of the 
union would be born neither in any year nor in any month. 
Nut turned to the god of wisdom, Thoth, for counsel. Thoth 
played a game of dice with the Moon-goddess, and won 
from her y^th part of of her light out of which he made 
five extra days. To appease Ba the Sun-god, these five 
days were given to him, and his year gained by five days 
while the Moon-goddess's year lost five days. The extra 
five days in the solar year were not attached to any month, 
which continued to have 30 days as before ; but these days 
came at the end of the year, and were celebrated as the 
birthdays of the gods born of the union of Seb and Nut, 
viz., Osiris, Iais, Nephthys, Set and Anubis, five chief gods 
of the Egyptian pantheon." * 

Let us scrutinize the implications of this myth. 
This is tantamount to discarding the moo?i altogether as a 
time-maker, and basing the calendar entirely on the sun. 
This was a very wise step, for as has been found from 
ancient times, the moon is a very inconvenient time- 
marker. The Egyptians maintained the old custom 
of keeping months of 30 days' duration, and 12 months 
made a year. But five days (Epagomenai in Greek) were 
added to the year at the end, which were not attached 
to any month. They were celebrated as national 
holidays. Each month of the Egyptian calendar was 
divided into 3 weeks, each of 10 days (Decads). 

The names of the Egyptian months together with 
the dates of beginning of each month as they stood in 
22 B.C., are as follows : 

* Zinner— Qeschichte der Sternkunde, p. 3, 


Egyptian Calendar 

Julian Calendar 

1 Thoth 


29 August 

1 Phaophi 


d,o September 

1 Athyr 


28 October 

1 Choiak 


27 November 

1 Tybi 


27 December 

1 Mechir 


26 January 

1 Phamenoth 


25 February 

1 Pharmuthi 


27 March 

1 Pachon 


26 April 

1 Payni 


26 May 

1 Epiphi 


25 June 

1 Mesori 


25 July 

(1 Epagomenai 5) 

24 August 

The year was divided into three seasons, each of 
four months : Flood time, Seed time and Harvest time. 

But the Egyptians soon found that even a year of 
365 days did not represent the correct length of the 
year, which, as we now know, is nearly 365J days. 
This fact they appear to have discovered in two 
different ways : 

(1) from their measurement of the length of the 
year from heliacal risings of Sirius, and 

(2) from their long record of floods extending 
over centuries. 

The fixed star Sirius, which is the most brilliant 
star in the heavens, was early associated with the chief 
goddess of the Egyptian pantheon, Isis> and was the 
subject of observation by her priests. The day of its 
first appearance on the eastern horizon at day-break 
(heliacal rising) appeared to have been carefully 
observed, and then on every subsequent day, its posi- 
tion in the sky at sunrise used to be noted. It was 
found that gradually it got ahead of the sun, so its 
appearance on the horizon would be observed sometime 
before sunrise, and on every successive sunrise, it 
would be found higher up in the heaven. After about 
a year it would be seen in the western horizon at 
sunset for a few days till it could no longer be traced. 
The Egyptians found as a result of long periods of 
observation, that it came again to the horizon at day 
break at the end of 365^ days, not 365 days. If on one 
year, the heliacal rising of Sirius took place on Thoth 1, 
(Thoth was the name of the first month of the year) 
four years later it would take place on Thoth 2, and 
forty years later on Thoth 11. As the mean interval 



of heliacal rising of Sirius at the latitude of Memphis 
was 365.25 days, the Egyptians concluded that the 
heliacal rising of Sirius would continue to move round 
the year in a complete cycle of ecu 1460 years ; called 
the Sothic cycle, after Sothis (Isis). They also appear 
to have found from observations over long periods of 
years that the Nile flood occurred not at intervals of 
365 days, but of 365^ days. 

On account of the deficiency of i day in the year, 
the year-beginning lost touch with the arrival of the 
Nile flood, though the temple priests had devised a 
method of finding out the interval between Thoth 1, 
and arrival of the Nile flood by observations of the 
heliacal rising of the bright star Sirius, identified with 
their chief goddess Isis. But they kept the knowledge 
to themselves. 

If the Egyptians carried out a reform of their calen- 
dar incorporating this fact, that the tropical year had a 
length of 365* days, their calendar could have been 
almost perfect. All that they had to do teas to take 6 
extra days instead of 5 every fourth year. But the 365- 
day year had so much soaked into the Egyptian mind, 
that this move for calendar reform was never adopted 
inspite of serious attempts by earlier Pharoahs, and 
later, a more serious one by the Graeco-Egyptian 
ruler Ptolemy Euergetes ( 238 B.C. ). But it became 
generally known that the correct length of the year 
was 365^ days. Fotheringham in his article on 'The 
Calendar" observes : 

An additional day was inserted at the close of the 
Egyptian year 23-22 B.C. on August 29 of what we call the 
Julian calendar, and at the close of every fourth year after- 
wards, so that the reformed or Alexandrian year began 
on August 30 of the Julian calendar in the year preceding 
a Julian leap year and on August 29 in all other years. 
The effect of this reform was to keep each Egyptian 
month fixed to the place in the natural year which it 
happened to occupy under the old calendar in the years 
2G-22 B.C. But the old calendar was not easily suppressed, 
and we find the two used side by side till A.D. 238 at least. 
The old calendar was probably the more popular, and 
was preferred by astronomers and astrologers. Ptolemy 
(150 A.D.) always used it, except in his treatise on annual 
phenomena, for which the new calendar was obviously more 
convenient. Theon in the fourth century A.D., though 
mentioning the old calendar, habitually used the new. 

Though not quite perfect, the Egyptian calendar 
was greatly admired in antiquity on account of its 
simplicity, for the length of the year and the months 
were fixed by definite rules and not by officials or 
pandits. The religious observances fell on fixed days 
of the month and at stated hours, which were fixed 
about 1200 B.C. 

On account of its simplicity, the Egyptian calen- 
dar was adopted by many nations of antiquity, and 
even sometimes by the learned Chaldeans and Greeks,. 
Fotheringham observes : 

"The Egyptian calendar was, upto the time of Julius- 
Caesar's reform of the Roman calendar in 46 B.C., the only 
civil calendar in which the length of each month and of 
each year was fixed by rule instead of being determined by 
the discretion of officials or by direct observation. If the 
number of years between two astronomical observations, 
dated by the Egyptian calendar, was known, the exact 
number of days could be determined by a simple calculation. 
No such comparison could be made between dates referred 
to any other civil calendar unless the computer had access 
to a record showing the number of days that had actually 
been assigned to each month and the number of months that 
had actually been assigned to each year. It is true that the 
Egyptians did not use a continuous era, but were content to 
number the years of each reign separately, so that there was. 
a difficulty in identifying a particular year, but the astronomers 
of the Ptolemaic age rectified this by the introduction of 
eras.* The simplicity and regularity of the Egyptian 
calendar commended it to astronomers, who found it 
excellently adapted to the construction of tables that could 
be readily applied and used even for a remote past or for 
a distant future without any fear that the system by which 
time was reckoned in the tables might not coincide with the 
system in actual use. In the second century B.C. we find 
Chaldean observations, sometimes nearly six centuries old, 
reduced to the Egyptian calendar in the works of 
Hipparchus (126 B.C.), who observed not in Egypt but at 
Ehodes, and cited from him by the Egyptian Ptolemy in 
the second century of our era ; we also find in the second 
century B.C., an Athenian observation of 432 B.C. reduced 
to the Egyptian calendar oh an inscription found at Miletus, 
which appears to represent the work of the astronomer 
Epi genes", t 

This calendar survives in a slightly modified form 
in the Armenian calendar, the three first months of 
the old Egyptian year corresponding exactly with the 
three last months of the Armenian year. The 
Alexandrian calendar is still the calendar of Abyssinia 
and of the Coptic Church, and is used for agricultural 
purposes in Egypt and other parts of northern Africa. 


The story of the calendar in Egypt has been given 
in full, because the ancient Egyptians evolved a very 
. simple and convenient calendar which, as mentioned 
before, would have been almost perfect (provided the 
year was taken to consist of 365J days instead of 365 
days). This was rendered possible by their bold initia* 

* The Nabonassar Era— vide § 3.4. 

+ Article on *The Calendar', Nautical Almanac, 1935. , 



tive of discarding the moon as a time-marker. But 
people in the remaining parts of the civilized world 
(e.g., in Babylon, Greece, India and China) in ancient 
and moderm times, retained tne moon and preferred 
the more complex luni-solar calendars described 
in Chap. III. This was rather fortunate, for if their 
rulers had adopted the Egyptian calendar, the priest- 
astronomers of ancient nations, particularly of 
Babylon, would never have taken to observation 
of the sun, the moon, and the planets, and tried 
to evolve mathematical formulae for predicting their 
positions amongst stars in advance (the Ephemerides) 
which form the basis on which our astronomical 
knowledge has been built up ; for the Egyptian 
calendar was evolved simply from results of 
experiences extending over centuries, and required 
almost no astronomical sense, or observations either 
of the sun, the moon and stars, except the heliacal 
rising of Sirius. It was simple and convenient, but 
like many perfect things, it killed intellectual curiosity. 

But as will be described in Chap. Ill, the luni-solar 
calendar is a very complex thing, and has taken in- 
finite variations in different regions. Hence the 
simple Egyptian calendar appealed to many nations 
of antiquity as well as of modern times. We have 
related the case of the Greek astronomers Hipparchos 
and Ptolemy who preferred the Egyptian method of 
date-recording to the Greek methods. This was, 
however, not the solitary instance. 


The great Iranian conqueror Darius (520 B. C), 
whose empire comprised Egypt, Mesopotamia, Syria 
and Asia Minor, besides his native country of Iran, 
certainly came into contact with the diverse calendars 
of older civilizations, but he appears to have preferred 
the Egyptian calendar to the more complex Babylo- 
nian calendar, and introduced it in his vast empire. 

But the astronomers of Darius made correction of 
the deficit of i day of the year in another way. 
They had all years of 365 days, but used an interac- 
lary month of 30 days in a cycle of 120 years. 

All the names of the old Iranian months and 
details of their calendar are not available now. The 
month-names as far as could be traced are stated 
below : — 

1. Thuravahara 

2. Thaigraci 

3. Adukani 

5. Garmapada 

7. Bagayadi 


9. Atriyadija 

10. Anamaka 

11. Margazana 

12. Viyachna 

The Persians did not have weeks or decads, but 
named * the successive days of the month serially 
according to their gods or religious principles, as 
below : — 



Nearest Vedic 

1. Ahurahe mazdao 


2. Vanheus mananho 


3. Ashahe vahistahe" 


4. Kshathrahe vairjghe* Shatvalro 

O. opeiltd.J<HJ cini.ia.njio 


6. Haurvatato 


7. AmeretatO 



8. Dathusho 

Dln-i-pavan AtarO 

9. SthrO 



10. Apam 



11. Hvarekshaetahe* 


12. Maonho 


13. Tistrjehe- 


14. Geus 


15. Dathusho 

Dln-i-pavan Mitro 

16. Mithrahe* 



17. Sraoshahe 


18. Rashnaos 


19. Fravashinam 


20. Verethraghnahe 



21. RamanO 

Ram ^ 

22. Vatahe 


23. Dathusho 

Din-i-pavan DinO 

24. Daenajao 


25. Ashois 


26. Arstato 


27. AsmanO 


28. ZemO 


29. Mathrahespentahe* 


30. Anaghranam 


After the Islamic conquest of Persia 

in 648 A.D., 

the purely lunar calendar of Islam (Hejira) was 
imposed on Persia, but it does not appear to have 
been liked by the native Iranians. 

In 1074-75 the Seljuq Sultan Jelal Uddin Melik 
Shah called upon the celebrated Omar Khayyam and 
seven others to reform the old Persian calendar. 
The calendar as reformed by them was called Tarikh- 
i-Telali, its era was the 10th Ramadan ^ of Hejira 



471- 16th March, 1079 A.D. There are many 
interpretations of the Jelali reform, the modern 
interpretation being 8 intercalary days in 33 years, 
giving the length of the year as 365.24242 days. The 
year started from the day of or next to vernal equinox. 

The Parsees in India, the followers of the Prophet 
Zarathustra are the descendants of Iranians who took 
shelter in India on the. conquest of Persia by the 
Arabs. The following details about their calendar 
is reproduced from Encyclopaedia Britannica (14th 
edition), Parsees : — 

The Parsees of India are divided into two sects, the 
Shahanshahis and the Kadmis. They differ as to the correct 
chronological date for the computation of the era of 
Yazdegerd, the last king of Sassanian dynasty, who was 
dethroned by the caliph Omar about A.D. 640. This led to 
the variation of a month in the celebration of the festivals. 
The Parsees compute time from the fall of Yazdegerd. Their 
calendar is divided into twelve months of thirty days each ; 
the other five days, being added for holy days, are not 
counted. Each day is named after some particular angel of 
bliss, under whose special protection it is passed. On feast 
days a division of five watches is made under the protection 
of five different divinities. In midwinter a feast of six days 
is held in commemoration of the six periods of creation. 
About March 21, the vernal equinox, a festival is held in 
honour of agriculture, when planting begins. In the middle 
of April a feast is held to celebrate the creation of trees, 
shrubs and flowers. On the fourth day of the sixth month 
a feast is held in honour of Sahrevar, the deity presiding 
over mountains and mines. On the sixteenth day of the 
seventh month a feast is held in honour of Mithra, the deity 
presiding over and directing the course of the sun, and also 
a festival to celebrate truth and friendship. On the tenth 
day of the eighth month a festival is held in honour of 
Farvardin, the deity who presides over the departed souls of 
men. This day is especially set apart for the performance 
of ceremonies for the dead. The people attend on the hills 
where the *' towers of silence" are situated, and in the sagris 
pray for the departed souls. The Parsee scriptures require 
the last ten days of the year to be spent in doing deeds 
of charity. 

In modern Iran when Riza Shah Pahlavi came to 
power in 1920, he instituted a reform of the existing 
Muslim calendar abandoning the strictly lunar 
reckoning and introducing purely solar year restoring 
the early Persian names which had never fallen 
entirely out of use. 

The names of the months, and their lengths are 
as follows : 

Parvardin-mah (31) begins 21 or 22 March 
Ardibahisht-mah (31) „ 21 or 22 April 
Khordad-mah/{31) „ 22 or 23 May 

Tir-aiah (31) M 22 or 23 June 

Mordan-mah (31) 
Shartvar-mah (31) 
Mehr-mah (30) 
Aban-mah (30) 
Azar-mah (30) 
Dai-mah (30) 
Bahman-mah (30) 
Esfand-mah (29, 30) 

begins 23 or 24 July 

23 or 24 August 
23 or 24 September 
23 or 24 October 
22 or 23 November 
22 or 23 December 
21 or 22 January 
20 or 21 February 


The Egyptian calendar attracted the notice of 
the calendar committee of the French Revolutionary 
Government (1789-1795) who wanted to replace 
Religion by Reason. The committee consisted, amongst 
others, the great mathematicians Laplace and Lagrange 
and the poet d'Eglantine. Laplace proposed that the 
year 1260 A.D,, when according to his calculations the 
equinoctial line ivas perpendicular to the apse line of 
the Earth's orbit should be taken the starting point of 
the French Revolution Era in place of a hypothetical 
year of Chrisfs birth. But the calendar committee 
did not agree with him but started the era of the 
glorious French revolution, with the autumnal 
equinox day of 1792 A.D., as this was nearest in date 
to the outbreak of the revolution. Sentiment proved 
stronger than cold scientific reasoning. 

French Revolution Calendar 

( 1792 Sept. 22 to 1806 ) 
( The Months consist of 30 days each ) 


Brumaire : 
Frimaire : 

Nivose : 
Pluviose : 
Ventose : 

7. Germinal 

8. Floreal : 

9. Prairial : 


Grape gathering 








Month beginning 

Sept. 22 
Oct. 22 
Nov. 21 



10. Messidor : 

11. Thermidor 

12. Fructidor : 

Day of Virtue 
„ Genius 
„ Labour 
„ Opinion 
„ Rewards 



March 21 
April 20 
May 20 

June 19 

July 19 

Aug. 18 

Sept. 17 

* 18 

,, 19 

■» 20. 

« 21 



The seven-day week was abandoned for a week of 
10 days. The month names were invented by the poet 
member of the committe. The last five days were 
dedicated to the service of the poor ( Sans-Culottides ) 
and did not form part of any month. 

After 13 years of service, the French Revolution 
calendar was abolished by Napoleon Bonaparte, then 
emperor of France, as part of his bargain with the 
Roman Catholic Church for his coronation by the Pope. 


(The Christian Calendar) 

What is now known as the Christian calendar, and 
used all over the world for civil purposes, had originally 
nothing to do with Christianity. It was, according to 
one view, originally the calendar o£ semi-savage tribes 
of Northern Europe, who started their year sometime 
before the beginning of Spring (March 1 to 25) and had 
only ten months of 304 days ending about the time of 
winter solstice (December 25), the remaining 61 days 
forming a period of hybernation when no work could 
be done due to the onset of winter, and were not 
counted at all. The city state of Rome also had 
originally this calendar, but several corrections were 
made by the Roman Governments a -^t epochs 

and the final shape was given to it by Julius Caesar in 
46 B:C ; the calendar so revised is known as the Julian 

As already stated, this calendar originally had 
contained ten months from March to December 
comprising 304 days. It may be regarded as certain 
that the months were lunar. The second Roman king 
of the legendary period, Numa Pompilius, is supposed 
to have added two months (51 days) to the year in 
about 673 B.C., making a total of 355 days ; January 
(named from the god Janus, who faced both ways) now 
began the year, and February preceded March, which 
became the third month. The number of days of the 
months were 29, 28, 31, 29, 31, 29, 31, 29, 29, 31, 29, 29. 
Adjustment of the year to the proper seasons was 
obtained by intercalation of a thirteenth month of 
actually 22 or 23 days* length (called Mercedonius) 
after two years or three years as was considered nece- 
ssary, and was inserted between February and March.* 
Had the intercalation been applied regularly at alter- 
nate years the additional days in four years would 
have been 45 (22 + 23) or Hi days per year on average, 

* Id fact, the intercalary month consisted sometimes of 27 day $ 
and sometimes of 28 days and was inserted after February 23. Th 
last five days of February, which were due to be repeated after ti i 
close of the intercalary month, were not actually repeated, result -h-.g 
in the intercalation of 22 or 23 days only. 

and so the year-length would have been 366£ days, 
only one day in excess of the correct length. But as 
the intercalation was applied tather arbitrarily some- 
times after two years and sometimes after three years, 
the year-beginning gradually bhifted and the year 
started before the arrival of the proper seasons. 

The days of the month in the Roman calendar were 
enumerated backwards from the next following Kalends (1st 
of month), Nones (5th of month, except in the 31-day months, 
when the 7th of month), or Ides (13th of month, except in 
the 31 -day months, when the 15th of month). Ihe day 
after the Ides of March, for instance, would be expressed as 
17 days before the Kalends of April. 

The Romans upto 45 B.C. apparently had rather 
a vague idea of the correct length of the year. 
Julius Caesar after his conquest of Egypt in 44 B. C. 
introduced the leap-year system on the advice of 
Egyptian astronomer Sosigenes, who suggested that 
the mean length of the year should be fixed 
at 365i days, by making the normal length of the 
year 365 days and inserting an additional day every 
fourth year. At the same time the lengths of the 
months were fixed at their present durations. The 
extra day in leap years was obtained by repeating the 
sixth day before the Kalends of March. The name 
Quintilis, the 5th month from March, was changed to 
July (Julius) in 44 B.C. in honour of Julius Caesar, and 
the name Sextilis was changed to August in 8 B.C. 
during the reign of his successor, Augustus, and in 
honour of him. There is a very widespread idea that 
the durations, of July and August were fixed at 31 days 
each in order to please 1 the two Roman dictators 
Julius Caesar, and Octavious Caesar, also called 
Augustus, and for this purpose the two extra days were 
cut off from February, thus reducing its duration to 
28 days. It is a nice story, but does not appear to 
have been critically probed. 

Owing to the drifting of the year-beginning, the 
year 46 B.C. started about 90 days before the proper 
seasons. The months were first brought back to their 
correct seasons by giving the year corresponding to 
46 B.C., a normal intercalation of 23 days after February 
and then inserting 67 additional days between 
November and December. This year therefore contai- 
ned 445 days in all and is known as the 'year of 

But the perfect calendar was still a long way off. 
Caesar wanted to start the new year on the 25th 
December, the winter solstice day. But people resisted 
that choice because a new-moon was due on January 1, 
45 B.C. and some people considered that the new-moon 
was lucky. Caesar had to go along with them in their 
desire to start the new reckoning on a traditional lunar 



The Julian calendar spread throughout the Roman 
empire and survived th$ introduction of Christianity. 
But the Christians introduced their c^wn holidays 
which were partly Jewish in origin and for, this, luni 4 - 
solar and week-day reckonings had to be adopted. 

Origin of the Seven-day Week 

Historical scholarship has shown that unlike, the 
year and the month, the seven-day week is an artificial 
man-made cycle. The need for having this short 
cycle arose out of the psychological need oi mankind 
for having a day of rest and religious service after 
protracted labour extending over days. The seven-day 
week with a sabbatical day at the end, or something 
similar to it, is needed not only by God Almighty, but 
also by humbler toiling men. But there has been no 
unanimity of practice. 

As already stated, the ancient Egyptians had a ten- 
day week. The Vedic Indians had a six-day week 
The ancient Babylonians who started the month on the 
day after new-moon, had the first, eighth, fifteenth, 
and the twenty-second day marked out for religious 
services. This was a kind of seven-day week with 
sabbaths, but the last week might be of eight or nine 
days' duration, according as the month which was 
lunar had a length of 29 or 30 days. The ancient 
Iranians had a separate name for each day of the 
month, but some days, at intervals of approximately 
seven, were marked out as Din-i-Parvan, for religious 
practices. The pattern followed appears to have been 
similar to the Babylonian practice. The continuous 
seven-day week came into general use sometime after 
the first century A.D. It was unknown to the writers 
of the New Testament who do not mention anything 
about the week day on which Christ was crucified or 
the week day on which he is alleged to have ascended 
to Heaven. The fixing of Friday and Sunday for these 
incidents is a later concoction, dating from the fifth 
century after Christ. All that the New Testament 
b(Qoks say is, that He was crucified on the day before the 
Hebrew festival of Passover which used to be celebrated 
and is still celebrated on the full-moon day of the 
month of Nisan. 

The continuous seven-day week was evolved on 
astrological grounds by unnamed astronomers who 
may have been Chaldean or Greek at an unknown 
epoch, butbefore the first century A.D. The Jews 
ad&pted it as a cardinal part of their faith during 
days of their contact with the Chaldeans. It is not their 
invention. We give a short story of this invention, as 
it is generally believed. But it may riot be quite 
accurate in all details. 

Invention of the Seven- day Week 

Much of ancient astronomical knowledge is due to 
Chaldean astronomers who flourished between the 
seventh century B.C. and the third century A.D., as 
related in §4*7. They gave particular attention to the 
study of the movement of the sun, the moon and 
the planets, which they identified with their gods, 
because they thought that destiny of kings and states 
were controlled by the gods, i.e., by the planets, 
and attached the greatest importance to the observa- 
tion of the position and movement of planets. They 
attached magical value to the number 'Seven' which 
was the number of planets or gods controlling human 

In 'Planetary Astrology', the sun, the moon and 
the five planets, were identified with the chief gods of 
the Babylonian pantheon^as given below : 

Planets Babylonian 


Iheir function 


Saturn . 

. . .Ninib 

God of Pestilence and 




. .Marduk , . . 

King of Gods. 



Nergal . . . 

God of War. 


Sun , . 

Shamash . . . 

God of Law & Order or 



Goddess of Fertility. 


God of Writing. 


God of Agriculture. 

These seven gods, sitting in solemn conclave, were 
supposed to control the destinies of kings and 
countries, and it was believed that their will and 
judgement with respect to a particular country or its 
ruler could be obtained from an interpretation of the 
position of the seven planets in the heavens, anfl the 
nature of motion of the planets (direct or retrograde). 

The Chaldean god-names are given in the second 
column, and the functions they control in the third 
column. Their identification with the Roman gods .is 
given in the first column. The planets* * were put 
in the order o^ their 'supposed distances from .the earth. 

Further, the day was divided into 24 hours, and 
each of the seven gods was supposed to keep watch 
on the world over each hour of the day in rotation. 
The particular day was named after the god who 
kept watch at the first hour. Thus on Saturday, the 
watching god on the first hour was Saturn, and 
the day was named after him. The succeeding 

♦Planets used nol in modern sense but m the old sense of & tvavderr 
ing heavenly body. 



hours of Saturday Were watched by the seven gods 
in rQtation as- follows :~ 


Hours 12 3 4 5 6 7 8.. .14 15 22 23 24 25 

God Watching 1 2 3 4 5 6 7 1... 7 1 1 2 3 4 (Sun) 
The table shows the picture for Saturday. On 
this day, Saturn keeps watch at the first hour, so the 
day is named after him. The second hour is watched 
over by (2) Jupiter, third by (3) Mars and so on. 
Saturn is thus seen to preside at the 8th, 15th and 
22nd hours of Saturday. Then for the 23rd, 24th and 
25th hours come in succession (2) Jupiter, (3) Mars 
and (4) Sun. The 25th hour is the first hour of the 
next . day, which was accordingly named after the 
presiding planet of the hour, vwr M No. 4 which is 
Sun. We thus get Sunday following Saturday. If 
we now repeat the process, we get the names of the 
week days following each other, as follows . 

Saturday, Sunday, Monday, Tuesday, 
Wednesday, Thursday, and Friday. 


C Moon 

Fig. 1— The order of week-days derived from the order of planets. 
Saturday followed by Sunday, then Monday and so on. 

The Jews, it may be mentioned*, reckon the days 
by ordinal numbers— the first, seconds seventh 
day. The "first day is Saturday. V ' 

The seven-day week, from the account of its origin 
is clearly based on astrological ideology. The conti- 
nuous seven-day week was unknown to the classical 
Greeks, the Romans, the Hindus, and early Christians. 
It was introduced into the Christian world by an edict 
of the Roman emperor Constantine, about 323 A.D., 
who cbanged the Sabbath to the Lord's Day (Sunday), 
the week-day next to the Jewish Sabbath. Its 
introduction into India is about the same time and 
from the same sources. The week-days are not 
found in earlier Hindu scriptures like the Veda s or 

the classics like the great epic Mahabharata. They 
occur in inscriptions only from 484 A.D., but not in 
inscriptions of 300 A.D. Even now, they form but an 
unimportant part in the religious observances of the 
Hindus which are determined by the moon s phases. 

It can therefore be said that the unbroken seven- 
day week was not a part of the religious life of any 
ancient nation, and it is not, even now, part of the 
religious life of many modern nations. It is a man-made 
institution introduced on psychological grounds, and 
therefore can be or should be modified if that leads 
to improvement and simplification of human life. 

The Christian Era 

The present Christian era came into vogue much 
later. About 530 A.D., the era-beginning was fixed 
from the birth year of Christ which was fixed after 
a certain amount of research by the Scythian Bishop 
Dionysius Exiguus and Christ's birth day (Christmas) 
was fixed on December 25 which was the Julian date 
for the winter solstice day and the ceremonial birth 
day of the Persian god Mithra in the first century B.C. 
The discovery of a Roman inscription at Ankara shows 
that King Herod of the Bible who is said to have 
ordered the massacre of innocents was dead for four 
years at 1 A.D., and therefore Christ must have been 
born on 4 B.C., ox somewhat earlier. 


The Julian year of 365.25 days was longer than 
the true year of 365.2422 by .0078 days, so the winter 
solstice day which fell on December 21 in 323 A.D. f 
fell back by 10 days in 1582 A.D. and the Christmas 
day appeared to be losing all connections with the 
winter solstice. Similar discrepancy was also noticed 
in connection with the observance of the Easter.* 
Various proposals were made for correcting the 
error and the Council of Trent which assembled in 
1545 authorised the Pope to deal with the matter. 
When in 1572, Gregory XIII became Pope, these 
schemes were considered and the plan that was most 

* Easter, the^nost joyous of the Christian festivals, is observed 
annually throughout Christendom in commemoration of the resurrec- 
tion of Jesus Christ, on the first Sunday after the full-moon 
following the vernal equinox day. The last days of Christ coincided 
with the Passover fast of the Jews and his death fell upon the day 
of the feast of the Passover, on the 14* day of the month of Nisan. 
As the date of Easter is associated with the moon's phased as well 
as the vernal equinox day, it is a movable festival, falling anywhere 
between March 22 and April 25. A movement is going on for 
narrowing down the range of variation of the Easter day ; m 1928 
the British Parliament passed the Easter Act, which contingent 
upon its acceptance internationally, fixed Easter day as the first 
Sunday after the second Saturday in April, falling between April 
9 and 15. {Vide Encyclopaedia Britannica> Easter). 



favoured was the one that had been proposed by 
Aloysrus Lilius, a Neapolitan physician. In 1582, Pope 
Gregory XIII published a bull instituting the revised 
calendar and ordained that Friday, October 5 of that 
year was to be counted as Friday, October 15. For 
the future, centurial years that were not divisible by 
400 were not to count as leap-years ; in consequence 
the number of leap-years in 400 years was reduced 
from 100 to 97 and the year-length of the calendar 
thus became 365*2425 days, the error being only one 
day in 3300 years. 

The Gregorian reformation of the calendar was 
at once adopted by the Catholic states of Europe, 
but other Christian states took longer time to accept 
it. In Great Britain it was officially introduced in 
1752. As the error had by that time amounted to 
11 days, the September of 1752 was deprived of these 
days and 3rd September was designated as the 14th 
September. In some countries the Gregorian calendar 
was not adopted until the present century. China 
and Albania adopted it in 1912, Bulgaria in 1916, 
Soviet Russia in 1918, Roumania and Greece in 1924, 
and Turkey in 1927. The rules for Easter which 
were revised on the basis of the Gregorian calendar 
have not been adopted by the Greek orthodox 

Inspite of its wide use, the Christian or Gregorian 
calendar is a clumsy and inconvenient system of time- 
reckoning on account of the arbitrary length of its 
months ranging from 28 to 31. With a view to 
reforming it many schemes have been proposed, but 
the one deserving of serious consideration is the new 
World Calendar advocated originally by the Italian 
astronomer Armellini in 1887 and adopted by the 
World Calendar Association, Inc., which has its head- 
quarters in New York (630, Fifth Avenue,, New York 
20, N. Y), under the able presidentship of Miss 
Elisabeth Achelis * 

In the ecclesiastical calendar some holy days are 
observed on fixed days of the year, others known as 
movable festivals are observed on fixed days of the 
week. Most of these are at fixed intervals before or 
after Easter day. When the Easter day of any year 
is fixed, the dates of other movable festivals can 
accordingly be ascertained. The Council of Nice 
convened in 325 A.D. adopted the rule for fixing the 
date of Easter — it was to fall on the first Sunday after 
the 14th day of the moon (nearly full moon) which 
occurs on or immediately after March 21. In fact 
there are certain special tables for determining the 

* She had been devoting her services ungrudgingly for the 
cause of calendar reform for the last twenty-five years, and also been 
publishing a 'Journal of Calendar Reform* since then. 

Easter day, based on the mean length of the lunar 
month, and the determination does not require any 
advance calculation of moon's position. The following 
are the principal holidays dependent on the date of 

Days before Easter 

Septuagesima Sunday 63 

Quinquagesima „ 49 

Ash Wednesday 46 

Quadragesima Sunday 42 

Palm Sunday 7 

Good Friday 2 

Days after Easter 

Low Sunday 7 

Rogation Sunday 35 

Ascension Day 39 

Whit Sunday 49 

Trinity Sunday 56 

Corpus Christi 60 


As already stated the Gregorian calendar is' a most 
inconvenient system of time-reckoning. The days of 
the months vary from 28 to 31 ; quarters consist of 90 
to 92 days ; and the two half-years contain 181 and 184 
days. The week-days wander about the month from 
year to year, so the year and month beginnings may fall 
on any week-day, and this causes serious inconvenience 
to civic and economic activities. The number of 
working days per month varies from 24 to 27, which 
creates considerable confusion and uncertainty in 
economic dealings and in the preparation and analysis 
of statistics and accounts. The present Gregorian 
calendar is therefore in dire need of reform. 

The question of resolving these difficulties had 
been under consideration for more than the last 100 
years. In 1834, the Italian Padre Abbe' Mastrofini 
proposed the Thirteen-Month Calendar, which was 
strongly advocated by the positivist philosopher August 
Comte. But this calendar could not attract much 
attention and consequently it was abandoned. The 
plan of reform which has received the most favourable 
comments is, as mentioned earlier, that of the World 
Calendar Association. 

Let us explain the ideas behind this movement : 

Calendars are used for regulating two essentially 
distinct types of human activities, viz., 

(a) Civic and administrative, 

(b) Social and religious. 

In ancient and medieval times, different countries 
and religions had developed their characteristic calen- 
dars to serve both purposes, but in the modern age, 
due to historic reasons, almost all countries use : 

(a) the Gregorian calendar for regulation of 
civic and administrative life, 

(b) their own characteristic calendars for regu- 
lation of social and religious observances. 

0. B. — 80 



For example, India uses the Gregorian calendar for 
civic and administrative purposes, but various, luni-solar 
calendars for fixing up dates for religious festivals of 
Hindus in different states. The Islamic countries also 
follow the same practice — Gregorian calendar for civic 
and administrative purposes, but the lunar calendar 
for religious purposes. 

Even in Christian countries, which apparently use 
the Gregorian calendar for both purposes, in actual 
practice, some additional time-reckonings have to be 
done for fixing the date of Easter and other holi- 
days which move with it. These reckonings constitute 
the ecclesiastic calendar, and are survival of earlier 
luni-solar calendars. 

The disadvantages of the Gregorian calendar as 
used for, civic and administrative purposes are : 

(a) that the years and months begin on different 
week days, 

(b) that months are of unequal length—from 28 
to 31 days — and they start on week-days 
which are most changeable. 

This happens because a normal year of 365 days 
consists of 52 weeks plus one day ; and a leap-year 
coming every fourth year, has 366 days, and consists of 
52 weeks plus 2 days. If a normal year begins on a 
Sunday, the next year will start on Monday, and the 
year after a leap-year will jump two week-days. 

This causes a most undesirable wandering of the 
^week-day on which the year begins, as is seen for the 
Tiext few years. This year 1954, has started on a 
Friday. We shall have 

1955 starting on Saturday 

1956 „ „ Sunday 

1957 „ „ Tuesday 

1958 „ „ Wednesday 

1959 „ „ Thursday 

1960 „ „ Friday 

1961 „ „ Sunday 

How much better it would be for civic and adminis- 
trative life if a system could be devised that every year 
should start on a Sunday ? 

The World Calendar Plan 

This is how the World Calendar Plan proposes to 
prevent this wandering of the starting-day of the * year. 
It is a very simple device. 

If from 1961, which starts on a Sunday, the last day 
of the year (ix. Dec. £1) which would be under the 
present system a Sunday, is called the Worldsday, that 
is, no week-day denomination is attached to it, then 
1962 also will start on a Sunday, and so will every year 
till the next leap-year 1964. On that year another 

additional day, the Leap- Year Bay, is inserted at the 
end of June, and have the usual Worldsday at the end 
of the year ; then 1965 will also start on a Sunday. 

So, by this simple device of having a Worlds-day 
at the end of every year and a Leap-Year Day at the 
end of June every fourth year, both without any 
week-day denomination, every year can be made to 
start on a Sunday, This will prove to be an inestimable 
advantage for the civic life of mankind. 

It is needless to add illustrations of the chaotic way 
in which the starting week-days of months vary. They 
are chaotic, because lengths of months vary from 28 
to 31. There is not the slightest scientific justifica- 
tion for these varying lengths. They are said to have 
been due to the caprice of two Roman dictators, or 
some other historical cause not yet clear. How much 
better it would be for civic purposes, if each month 
could start on a fixed day of the week ? 

The World Calendar plan proposes to put this right 
by dividing the year into four quarters, each of three 
months of 31, 30, 30 days' duration. According to this 

January, April, July, October would have each 
31 days, and start on Sunday, 

February, May, August, November would have each 
30 days, and start on Wednesday, 

March, June, September, December would have 
each 30 days, and start on Friday. 

If this plan be adopted, the calendar will be perpe- 
tual and fool-proof. What a welcome change it would 
prove when compared to the present chaotic and 
wandering calendar ? 

The year has to conform to the period of the sun, 
and this is covered by the leap-year rules, amended 
by Pope Gregory XIII in 1582. The leap-year rules 
introduced by the Iranian poet-astronomer Omar 
Khayyam in 1079, were more accurate, but less 
convenient. The Gregorian leap-year rules will 
cause a mistake of only one day in 3,300 years, which 
is trivial. 

As regards the duration of months, the World 
Calendar plan is a marked improvement on the 
chaotic lengths and starting days of months, inherited 
from the Julian calendar, which has been tolerated 
too long. The months of all the quarters are identical 
and have got 31, 30 & 30 days, commencing on 
Sundays, Wednesdays and Fridays respectively. Each 
month has thus got exactly 26 working days. It has 
retained the present 12 months, thus the four quarters 
are always equal, each quarter has 3 months or 13 
weeks or 91 days beginning on Sunday and ending 
with Saturday. 



The objections to the World Calendar plan come 
from several Jewish organizations, on the ground that 
the World Calendar plan interferes with the 
unbroken seven-day week, by introducing Worlds- 
day and Leap-year - Day without any week-day 
denomination. This, they say, will interfere with 
their religious life. 

As already shown, the religious sanction for the 
seven-day cycle is either non-existent, or slight, 
amongst communities other than the Jews, and even 
amongst them, it dates only from the first century A. D. 
The claims of certain Jewish Rabbis to prove that the 
seven-day week cycle has been ordained by God 
Almighty from the moment of creation which event, 
according to these Jewish Rabbis, took place on the 
day of the autumnal equinox, also a new moon day, 
is a fantastic conception of medieval scholars, which 
no sane man can entertain in these days of Darwin and 

The World Calendar plan has no intention of 
interfering with, the characteristic calendars of 
communities or nations. They can exist side by side 
with the World Calendar. For such communities as 
intend to maintain the continuous seven-day week, 
their religious week-days, including Sundays, would 
no doubt wander through the World Calendar week- 
days, and cause some inconvenience to the very small 

fraction of people who would want to observe their 
religious rites accprding to established usage. 

But these inconveniences can be adjusted by 
agreement, and it would be egoistical on the part of 
a particular community or communities to try to 
impede the passage of a measure of such great useful- 
ness to the whole of mankind on the plea that the 
World Calendar plan interferes with the continuous 
seven-day week. Calendars are based on Science, 
which everybody must bow to ; and on Convention, 
which may be altered by mutual consent. The 
unbroken seven-day week is a Convention^ but the 
World Calendar plan has proposed a far better Conven- 
tion, which should be examined on its own merits.* 

As a result of a request from the Government of 
India, the proposal of the World Calendar Reform 
had become the subject of discussion at the eighteenth 
session of the Economic and Social Council of the 
United Nations held at Geneva during June- July, 
1954. Professor M. N. Saha, F. R. S., Chairman, 
Calendar Reform Committee, attended the ECOSOC 
meeting at Geneva to explain the desirability of the 
proposed reform. 

* Being the full text of the address in support of the Indian 
proposal for World Calendar reform, by Prof. M. N. Saha, F.R.S- at 
the 18th Session of the Economic and Social Council of the United 
Nations, held at Geneva in June-July, 1954. 



S M T W T F S 

1 2 3 4 5 6 7 
8 9 10 11 12 13 14 
15 16 17 18 19 20 21 
22 23 24 25 26 27 28 
29 30 31 


S M T W T F S 

12 3 4 
5 6 7 8 9 10 11 
12 13 14 15 16 17 18 
19 20 21 22 23 24 25 
26 27 28 29 30 


S M T W T F S 

1 2 

3 4 5 6 7 8 9 
10 11 12 13 14 15 16 
17 18 19 20 21 22 23 
24 25 26 27 28 29 30 


S M T W T F 

12 3 4 5 6 7 
8 9 10 11 12 13 14 
15 16 17 18 19 20 21 
22 23 24 25 26 27 28 
29 30 31 


S M T 

T F S 

12 3 4 
5 6 7 8 9 10 11 
12 13 14 15 16 17 18 
19 20 21 22 23 24 25 
26 27 28 29 30 


M T W T F S 

1 2 

3 4 5 6 7 8 9 
10 11 12 13 14 15 16 
17 18 19 20 21 22 23 L, 
24 25 16 27 28 29 30 W| 


S M T W T F S 

1 2 3 4 5 6 7 
8 9 10 11 12 13 14 
15 16 17 18 19 20 21 
22 23 24 25 26 27 28 
29 30 31 


S M T W T F 

12 3 4 
5 6 7 8 9 10 11 
12 13 14 15 16 17 18 
19 20 21 22 23 24 25 
26 27 28 29 30 


s m T w t f s 

1 2 

3 4 5 6 7 8 9 
10 11 12 13 14 15 16 
17 18 19 20 21 22 23 
24 25 26 27 28 29 30 


S M T W T F S 

1 2 3 4 5 6 7 
8 9 10 11 12 13 14 
15 16 17 18 19 20 21 
22 23 24 25 26 27 28 
29 30 31 


S M T W T F S 

12 3 4 
5 6 7 8 9 10 11 
12 13 14 15 16 17 18 
19 20 21 22 23 24 25 
26 27 28 29 30 


S M T W T F S 

1 2 

3 4 5 6 7 8 9 
10 11 12 13 14 15 16 
17 18 19 20 21 22 23L- 
24 25 26 27 28 29 30 W| 

W <Worldiday, a World Holiday) ttttb 31 DtetuWr (365th day) and fottowi 30 Dtcim- 

ber mry yu». _ 
W (Lupytar Day. another World Holiday) «Q<»U 31 Jtmt and follow* 30 Jwo in too ytars. 

In this Improved Calendar : 

Every year is the same. 

The quarters are equal : each quarter has 
exactly 91 days, 13 weeks or 3 months ; the 
four quarters are identical in form. 

Each month has 26 weekdays, plus Sundays. 

Each year begins on Sunday, 1 January ; each 
working year begins on Monday, 2 January. 

Each quarter begins on Sunday,, ends on 

The calendar is .stabilized and perpetual, by 
ending the year with a 365th day that follows 
30 December each year, called Worldsday dated 
"W" or 31 December, a year-end world holiday. 
Leap-year day is similarly added, at the end of 
the second quarter, called Leapyear Day dated 
"W" or 31 June, another world holiday in 
leap years. 


The Luni-Solar and Lunar Calendars 


The Egyptians appear to have been the only 
cultural nation of antiquity who discarded the moon 
entirely as a time-marker. Other contemporaneous 
cultural nations, e.g., the Sumero-Akkadians of 
Babylon, and the Vedic Indians retained both the sun 
and the moon as time-markers, the sun for the year, the 
moon for the month. 

The Indian astronomers called the moon masakrt, 
(month-maker) and before the Siddhanta Jyotw time, 
the moon was considered more important as a time- 
marker than the sun (tide §5). It was the same with 
other nations too, for as Pannekoek remarks, we find 
the opinion written in the sacred books of many 
nations "For regulating time, the moon has been 

The retention of both the sun and the moon, 
however, gives rise to a multitude of problems, of which 
a fair summary is given by Pannekoek as follows.* 

"With all peoples of antiquity, the Indians, Babylonians, 
Jews, Greeks, we find the moon-calendar used ; the period 
of the moon, the regular sequence of the first appearance of 
the fine crescent moon in the evening sky, its growth to first 
quarter, to full moon, at the same time coming up later and 
filling the whole night, then the decrease to last quarter till 
its disappearance after the last thin crescent before sunrise 
was seen,— this regular cycle of the moon's phases in the 
period of 29i days was everywhere the first basis of 

"But the calendar could not be satisfactorily fixed with 
the establishment of the moon-cycle. In these ancient 
times, the people, the tribe, and the state was » political, 
spiritual and religious unity. Important events of society, 
the great agricultural performances, the beginning of the 
ploughing, the sowing or the harvesting were great popular 
festivals and at the same time chief religious ceremonies, 
when offerings were presented to the gods. The moon 
calendar had to adapt itself to the economic life of the 
people, which was governed by the cycle of seasons. Thus 
arose the practical problem of adapting the moon-period of 
29i days to the solar year of 365 days. Thin chief problem 
.of ancient chronology has been a mighty impulse to the study 
of astronomy, because it necessitated continuous observation 
of the sky" 

'~*~~i^r^'jis^ioSV <™d its influence upon the development 
of Astronomy' by Anton Pannekoek, published in the Journal of the 
Royal Astronomical Society of Canada, April, 1930. 

Twelve lunar months of 29£ days each, making a 
total of 354 days, fall nearly 11 days short of the solar 
year. In the next year, the beginning of each month 
occurs 11 days earlier, in three years 33 days will be 
lost.* To fix the same month to the same season 
always, there are no other means than after two or 
three years to intercalate a Thirteenth Month, number 
13, by repeating the last month of the year. 

The luni-solar adjustment which is next taken up 
is the first step to the solution of problems stated by 
Pannekoek, but it is not however the whole solution, 
for it leaves untouched the problem of correct predic- 
tion of the day when the crescent of the moon first 

appears after new moon in the western horizon. This 

will be taken up later (vide §4). 

Luni-solar adjustment can be satisfactorily made 

if we have accurate knowledge of the length of the 

tropical year, and of the mean length of the lunation. 

Let us see how these fundamental periods were 

determined in ancient times. 

Length ot Seasons and the Year 

The length of the year was obtained in Egypt, as 
we have already seen, from the recurrence of the Nile 
flood. In Babylonia, no such striking natural 
phenomena were available. It is very probable that 
the Babylonians early learnt the use of the gnomon, 
with the aid of which they could determine the 
cardinal days of the year : <oix. y the summer and winter 
solstices, and the two equinoxes coming in between. 

The lengths of the seasons were found by counting 
the number of days from one cardinal day to the next. 
The number may vary' by one day from year to year, 
and astronomers must have realized that the correct 
length of a season was not a whole number but was 
fractional. Probably the correct length was found by 
taking a large number of observations, and taking the 
mean. The following table shows the length of the 
seasons and of the year as found by ancient 

* The mean duration of ft lunar month consists of 29*530688 
days and twelve such lunations amount to 354*36706 days, while the 
length of a tropical solar year is 365*4220 days. The length of a 
lunar year thus falls short of the solar year hy 10.87514 days, and 
instead of there being exactly twelve lunar months in ft year, there 
are 12.36827 months. 




Table 2. — Showing the length of seasons. 

Euctemon Calippos Chaldean Correct 

values for 

(432 B.C.) (370 B.C.) (200 B.C.) 1384 B.C. 

























Total — 





The length of the year was also found by the same 
method. The solar year is the period between 
successive transitions of the sun through the same 
cardinal point, Neugebauer thinks that summer 
solstice was first used for this purpose in ancient 
times. But subsequently evidences are found of the 
use of other cardinal points. 

Thus we find that during the classical period in 
Babylon, the solar year started with the vernal 
equinox. But the Macedonian Greeks and the Jews 
started with the autumnal equinox. The west 
European countries appear to have started the solar 
year with the winter solstice. 

The number of days in a solar year would vary 
between 365 and 366. Probably the exact length was 
determined by counting the number of days between the 
year-beginnings separated by a large number of years 
and taking the mean. The Indian practice, followed in 
the Siddhantas, is to give the number of days in a 
Kalpa (a period of 4.32x10° years) from which one 
can find out the number of days in a year by simple 
division. This appears in modern times to be a rather 
cumbrous practice, but is probably reminiscent of 
taking the mean for a large number of years. 

In ancient times, people had not learnt to follow 
the motion of the sun in the starry heavens, so they 
were unaware of the difference between the ( sidereal 
year and the tropical year. But from their method of 
measurement, they unconsciously chose the correct, or 
the tropical year. 

Modern measurements show that the length of the 
tropical year is not constant, but is slowly varying. 
It is becoming shorter at the rate of "0001 days or 8*6 
sees, in 1600 years. 

So that in Sumerian times, the tropical year had 
a length of 365.2425 days. The present length is 
365-2422 days. 


The solar year has thus a pretty nearly constant 
value, but even the earliest astronomers appear to 
have observed, that the lunation, or the synodic period 
of the moon is not a constant, but is variable. As a 
matter of fact, the period varies from 29*246 to 29.817 
days— nearly fourteen hours. The observation of the 
actual motion of the moon formed the most formidable 
problem in ancient astronomy {vide §4). 

But all ancient nations show knowledge of an 
astonishingly correct value of the mean synodic period, 
which is known to be 29.530588 days. This is probably 
because they could count the number of days with 
fractions comprising a very large number of lunations, 
and therefore the mean value came out to be very 

With the aid of the knowledge of correct values of 
the length of the tropical year, and of the mean 
synodic period of the moon, it is possible to find out 
correct rules for luni-solar adjustment, as narrated 
below. But this could happen only at a later stage. 
The first stage was certainly empirical as is clearly 
indicated from a record of the great Babylonian king 
and law-giver Hammurabi (1800 B. C), which says that 
the thirteenth month was proclaimed by royal order 
throughout the empire on the advice of priests. All 
religious observances were forbidden during this 

It is not known however, what principles, if any, 
guided the king or rather his advisers in their selection 
of the thirteenth month, but most probably the 
adjustment was empirical, i.e., the month was discarded 
wlien the priests found 'from actual experience that 
the festival was going out of season. Many ancient 
nations who used the luni-solar calendar, do not 
appear to have gone beyond the empirical stage. 

Empirical Relations between the Solar and Lunar 
Periods : The Intercalary Months. 

The Chaldean astronomers (as the Babylonians 
were called after 600 B.C.) appear to have striven 
incessantly to obtain very accurate values for the 
mean lunation and the length of the solar . year, and 

* It is said that in ancient Palestine, the custom was that the 
Rabbis went to tjie fields and watched the time by their calendar for 
the ripening of wheat. * If the lunar month of Addaru (last month of 
the year) fell back too much towards winter, they would proclaim a 
second Addaru in that year, so that the first of Nisan would coincide 
roughly with the ripening of wheat 



work oat at the discovery of mathematical relation- 
ships between these two periods having the form- 

m lunar months =w solar years 
where both <m and n are integers. 

Let us describe some of these relations. 
The Octaeteris : This depends on the relation : 

8 tropical years ==2921 .94 days 
99 lunar months =2923.53 days. 

The difference is only 159 days in 8 years. We 
have used here the correct lengths of the two periods. 
The Babylonian values were slightly different. 

According to this relation, there were to be three 
extra or intercalary months in a period of 8 years, and 
festivals would fall approximately in the right seasons, 
if these three months were suitably excluded for 
religious observances. But the rule was only approxi- 
mate. In a few cycles, the discrepancy would be too 
large to be disregarded. 

According to the celebrated exponent of Baby- 
lonian astronomy, Father Kugler, this system was in 
vogue from 528 B.C. to 505 B.C., then there was an 
interval when they used to have 10 intercalary months 
in a period of 27 years. From 383 B.C., the Chaldeans 
used the 19-year cycle, based on the relation : 

19 solar years -6939.60 days 
235 lunar months =6939.69 days. 

There is a discrepancy of .09 days in 19 years, or a 
mistake of 1 day in 210 years. 

The 19-year cycle, with 7 intercalary months was 
used throughout the whole Seleucid times (313 B.C.- 
75 B.C.), as shown by Pannekoek. This system has 
not been superseded inspite of various attempts. 

These rules came into vogue at a time (383 B.C.), 
when Babylon had lost her independence and became 
a vassal state of the Persian empire of the Achemmids. 
We do not know what was the original calendar of 
pre-Acheminid Persia, but the great Acheminid 
emperor Darius preferred the simpler Egyptian solar 
calendar to the complex luni-solar calendar of Babylon. 
The population of Babylon could no longer depend 
upon the king to adjust the dates of their religious 
observances by royal decree, as happened in the time 
of Hammurabi (1800 B.C.). Probably therefore the 
priest-astronomers felt the need of mathematical rules 
which should take the place of royal decrees. 

Table 3.— The 19-year cycle. 

Cycle of 19 years showing Intercalary Months 

(Compiled from Pannekoek' 9 calculation of dates 
in Babylonian Tables of planets) 

Year in the 
19-year cycle 










Total no. of 











Tears of the 
Seleucidean Era 

134 153 172 

135 154 173 

136 155 174 

137 156 175 

138 157 176 

139 158 177 

140 159 178 

141 160 179 

142 161 180 

143 162 181 

144 163 182 

145 164 183 

146 165 184 

147 166 185 

148 167 186 

149 168 187 

150 169 188 

151 170 189 

152 171 190 

191 210 229 

192 211 230 

193 212 231 

194 213 232 

195 214 233 

196 215 234 

197 216 235 

198 217 236 

199 218 237 

200 219 238 

201 220 239 

202 221 240 

203 222 241 

204 223 242 

205 224 243 

206 225 244 

207 226 245 
2C8 227 246 
209 228 247 



N. B. Years marked * have a second Addaru, 
and years marked + have a second Ululu. 

312- Seleucidean era«Christian era B.C. 

(Jan. to Sept.) 

Seleucidean era -311 -Christian era A.D. 

(Jan. to Sept.) 

The 'Nineteen-year cycle* is generally known as 
the 'Metonic Cycle' after Meton, an Athenian 
astronomer who unsuccessfully tried to introduce it 
at Athens in 432 B.C. But there is no proof that it 
was used at Athens before 343 B.C. The question of 
'priority' of this discovery is therefore a disputed one. 


In addition to the Chaldeans, many other nations 
of antiquity, viz., the Vedic Indians, the Greeks, the 
Romans and the Jews and others used the luni-solar 
calendar, and had to make luni-solar adjustments. 
It will be tedious to relate how they did it, except 
in the case of the Vedic Indians (vide § 5). But the 
knowledge of the nineteen-year rule appears to have 
diffused to all countries by the first century of the 
Christian era. From this time onwards, the lunar 
months of different nations appear to be interchange- 
able. This is shown in the following Table No. 4. 

We have almost complete knowledge of the luni- 
solar calendars or the Babylonians during Seleucid 
times. The names of months with their normal lengths 
are shown in column (2) of the table. 



Table 4. — Corresponding Lunar months. 
Lunar Month-Names 













NISANNU (30) Artemesios 




(29) Daisios 




(30) Pancmps 




(29) Loios 




(30) Gorpiaios 




(29) Hyperberetrios 




(30) DIOS 


Margaslrsa Arah 


(29) Appclaios 




(30) Audynaios 




(29) Peritios 




(30) Dystros 




(29) Xanthicos 

Adar and 

The first Babylonian month Nisannu, started with 
30 days, and other months were alternately 29 and 30 
days. A normal year thus consisted of 354 days, but 
occasionally an extra day was added to the last month, 
and it became a year of 355 days. 

The effect of these intercalations was that the first 
month, viz., the month of Nisannu, never strayed for 
more than 30 days beyond the day of vernal equinox. 

As the table shows, the Babylonian year might be 
of 354, 355, 383, or 384 days duration, and occasio- 
nally it is said that they extended to 385 days. It 
was therefore impossible to calculate the number of 
days between two incidents, dated accoiding to the 
Chaldean calendar, unless the investigator had a table 
of past years showing the lengths of each individual 
year. Herein comes the superiority of the Egyptian 
system, where the number of days between two 
incidents, dated according to the Egyptian system, 
could be easily calculated. The two greatest astro- 
nomers of ancient times, Hipparchos and Ptolemy, 
therefore, preferred the Egyptian system of dating to 
the Chaldean or the Macedonian. 

The Macedonian Greeks used the months given 
in column (3) in their home land. When they settled 
in Babylon as rulers (313 B.C.), they continued to use 
the same months, but got them linked to Chaldean 
months. Their first month was Dios, which was 
the seventh month of Chaldeans. This was probably 
linked to the autumnal equinox in the same way as 
Nisannu was to the vernal equinox. The Macedonian 
year started six months earlier than the Chaldean year. 

The Macedonian months were used by the 
Parthians, the early Sakas, and the Kushans in India 
wihout change of name (vide § 5-5), and probably the 

month-lengths were also the same as in the Chaldean 
19-year system. When the Sakas and Kushans began 
to rule in India, from first century B.C., they used 
the Macedonian months alternatively with the Indian 
months which are shown in the first column. The first 
Indian season, Spring, however according to imme- 
morial Indian custom, has been on both sides of the 
vernal equinox ( — 30° to 30°), while in the Graeco- 
Chaldean system, the Spring started with vernal 
equinox (0°). The first Indian month is Caitra, the 
first of the spring months, and according to rules 
prevalent in Siddhantic times (300 A.D.), the month 
was to be always on the lower side of the vernal 
equinox, i.e., the beginning of lunar Caitra was to be on 
a date before the vernal equinox. It may be added that 
the Indian lunar months mentioned here are amanta 
or new moon ending. 


For accurate date-recording, we require besides 
the month and the day, also a continuously running 
era. But the era came rather late in human history. 
We find dated records of kings in Babylon from about 
1700 B.C. (Kassite kings). They used regnal years, 
lunar months, and the day of the lunar month. The 
ancient Egyptian records do not use any era, but 
sometimes the regnal years. But the use of regnal 
years is very inconvenient for purposes of exact 
chronology, because one has to locate the beginning 
of the reign of the king on the time-scale which often 
proves to be an extremely difficult problem, e.<?., in 
India, Emperor Asoke used regnal years, but it is a 
problem of nearly hundred years for archaeologists 
to find out the exact date of the commencement of 
his reign. This varies from 273 B.C. to 264 B.C. 

In the writings of the Greek astronomers Hippar- 
chos (140 B.C.) and Ptolemy (150 A.D.), we come across 
an era purporting to date from the time of one king 
Nabu Nazir of Babylon (747 B.C.), who is known to 
history, though this era is not used in records of the 
Babylonian kings themselves. 

The inference has been made, though without 
clear proof, that the Babylonian or rather Chaldean 
astronomers who were the earliest systematic observers 
of the heavenly bodies, get tired of the use of the 
regnal years, and felt the need of a continuously 
running era for precision in time-reckoning. They 
took advantage of a unique gathering of planets about 
Feb. 26, 747 B.C. when Nabu Nazir was reigning in 
Babylon to proclaim that the gods have ordained the 
'introduction of a continuously running era' ( Shy and 
Telescope, Vol. I, p. 9, April, 1942). 

But the use of the Nabonassar era appears to have 
been confined to astronomers. The kings continued 



to record events, in their regnal years as this had 
a great propaganda value for the royal family which 
they were unwilling to forego. 

It is now known that the other ancient eras, like 
that of the Greek Olympiads (776 B.C.) or the era of 
Foundation of Rome (753 B.C.) are extrapolated eras. 
The ancient Greek method of dating by Olympiads is 
of uncertain origin, but the system was critically 
examined by the Alexandrian chronologists, parti- 
cularly Eratosthenes (3rd century B.C.), the founder of 
scientific chronology. According to the Encyclopaedia 
Britannica, 14th edition, Greek chronology is not 
reliable till the 50th Olympiad (i.e. 576 B.C.). The 
era was therefore invented a long time after its alleged 
year of starting. The era of the Foundation of Rome 
had a similar history (see Encyclopaedia Britannic* 14th 
edition, Chronology). The starting years of these eras 
are suspiciously close to that of the Nabonassar era 
(747 B.C.). Probably both these eras were plagiarized 
from the era of Nabonassar after the savants of 
ancient Greece and Rome acquired the time-sense. 

It is noteworthy that Hipparchos and Ptolemy used 
neither the era of Olympiads nor the era of Foundation 
of Rome, nor Greek or Chaldean months which were 
lunar, but the Nabonassar era and the more con- 
venient Egyptian solar months. They preferred 
science to nationalistic chauvinism. 

The Seleucidean and other derived Eras 

The Seleucidean Era (the S. E. era) : The first 
continuously running era which ran into general 
circulation is that introduced to commemorate the 
foundation of Seleucus's dynasty and dates from the 
year when Seleucus occupied the city of .Babylon 
after defeating his rivals. There were two methods 
of counting, differing in the initial year and the first 
day of the year. 

According to the official (Macedonian) reckoning, 
the era started from the lunar month of Dios (near 
autumnal equinox) in the year (—311) A.D. or 312 B.C. 
The months had Macedonian names. 

According to the native Babylonian reckoning, the 
era started from the lunar month of Nisan (near 
vernal equinox) six months later than the starting of 
the Macedonian year. The months had Chaldean 
names, as given in Table No. 4. 

The Seleucid monarchs ruled over a vast empire 
from Syria to the borders of Afghanistan from 311 B.C. 
to 65 B.C. i.e., nearly for 250 years and under their 
rule, the knowledge of Graeco-Chaldean astronomy 
and time-calculations spread far and wide, ultimately 
reaching India, and profoundly modifying the indige- 
nous system in India. The use of Macedonian months 

spread over all these countries, as is apparent from 
contemporary inscriptions and coin-datings mentioned 
in § 5*5. The months were amanta, i.e., started after 
the new-moon was completed and were pegged on to 
the solar year which started on the day of the vernal 
equinox. The Nisan was the first lunar month after 
the vernal equinox. There were 7 intercalary months 
in a period of 19 years. The correspondence between 
Chaldean and Greek months and the position of the 
intercalary months have been worked out by Prof. 
Pannekoek between the years 134-247 of the Seleuci- 
dean era, as already given (vide § 3-2 and 3-3) along 
with their Indian equivalent lunar months. 

The Parthian Era 

Since the introduction of the Seleucidean era, the 
practice arose for a nation or a dynasty to start eras 
commemorating some great event in their national or 
dynastic life. The first in record is the Parthian era, 
and the story of its starting is well-known. The 
Seleucid emperors ruled the Near East from 312 B.C. 
imposing on the countries under their domination 
Greek culture, the Seleucidean era, and the Graeco- 
Chaldean system of time-reckoning. About 250 B.C., 
there were wide-spread revolts against Seleucid rule in 
Bactria, in Parthia (Eastern Persia), and other parts 
of the Near East. The revolt in Parthia was led by 
one Arsaces and his brother Tiridates who belonged 
to an Iranian tribe, which had adopted Greek culture. 
To commemorate their liberation from Seleucidean 
rule, the Parthians introduced an era, beginning 
64 years after the Seleucid era (i.e. 248 B.C.). But 
at first this era (Arsacid era) was only rarely used. 
The early Parthian emperors preferred to use on 
their coins the Seleucidean era, the Macedonian 
months, and the Graeco-Chaldean system of time- 
reckoning inscribed in Greek letters. In the first 
century A.D., there was a Zoroastrian revival, the 
S.E. was dropped in favour of the Parthian era and 
Pehlevi began to be used in place of Greek, though 
Macedonian month-names were still kept. 

Though kings bearing Parthian names ruled at 
Taxila about the first century B.C. to first century A.D., 
e.g., king Gondophernes, no clear evidence of the 
use of the Parthian era on Indian soil has yet 
been found. 

It is very likely that the Saka era, with its methods 
of calendar-reckoning, which came into vogue in 
India during the Siddhctnta Jyotisa times, was started 
by the Saka tribes when they attained prominence, 
and started an era of their own, in imitation of the 
Parthians. They, however, retained the Graeco- 
Chaldean method of lunar month-reckoning and 
probably the same system of intercalary months. 




The ancient Jewish calendar was lunar, the 
beginning of the month being determined by the first 
visibility of the lunar crescent. As the month-names 
show (col. 4 of the table No. 4 ), they were evidently 
derived from the Babylonian month-names excepting 
one or two, viz., Marheshvan and Tammuz. The day 
began in the evening and probably at sunset. The year 
used to begin with the spring month Abib or Nisan, 
the latter being the Babylonian name of the month 
which was adopted by the Jews in the post-exilic 
times. Intercalation was performed, when necessary, 
repeating the twelfth month f Adar which was then 
known as 'Veadar' followed by Adar. The year- 
beginning was subsequently changed and in the last 
century before Christ, it became the month of Tishri, 
corresponding to the Macedonian month of Bios. This 
must have been due to the desire or need to follow 
the practice of the ruling race. 

Originally there were no definite rules for inter- 
calation and for fixing up the beginning of the months. 
Because various religious festivals and sacrifices were 
fixed with reference to the beginning of the month, 
information about it was spread throughout the 
country by messengers and by signal fires on hilltops. 

About the 4th century A.D., fixed rules were 
introduced in the calendar and nothing was left to 
observation or discretion. Intercalation is governed 
by a 19-year cycle in which the 3rd, 6th, 8th f 11th, 
14th, 17th and 19th years have got an extra month. 
The actual beginning of the initial month of the year, 
vix., Tishri is obtained from the mea'n new-moon by 
complicated rules which are designed to prevent 
certain solemn days from falling on inconvenient 
days of the week. As a result, a common year may 
consist of 353, 354 or 355 days and an embolismic or 
leap-year of 383, 38*4 or 385 days. Ten of the months 
have got fixed durations of 29 or 30 days, as well as 
the intercalary month which contains 30 days, the 
other two varying according to the requisite length 
of the year. 

The Jewish Era of Creation 

The Jews use an Era {Anno Mun&i, libriath olum) 
or 'Era of Creation which is supposed to have been 
started from the day of creation of the world. We 
quote the following passages from Encyclopaedia 
Britanmca; 14th edition, 'Chronology, Jewish'. 

(l) The era is supposed to begin, according to the 
mnemonic Beharad, at the beginning of the lunar cycle on 
the night between Sunday and Monday, Oct. 7, 3761 B.C., 
at 11 hours Hi minutes P.M. This is indicated by be (beth, 

two, i.e., 2nd day of week), ha (he, five, i.e., fifth hour after 
sunset) and Bad (Besh, dalet, 204 minims after the hour). 

(2) In the Bible various eras occur, e.g., the Mood, the 
Exodus, the Earthquake in the days of King Uzziah, the 
regnal years of monarchs and the Babylonian exile. During 
the exile and after, Jews reckoned by the years of the 
Persian kings. Such reckonings occur not only in the Bible 
(e.g., Daniel viii, I) but also in the Assouan papyri. After 
Alexander, the Jews employed the Seleucid era (called 
Minyan Shetaroth, or era of deeds, since -legal deeds were 
dated by this era). So great was the influence exerted by 
Alexander, that this era persisted in the East till the 16th 
century, and is still not extinct in south Arabia. This is the 
only era of antiquity that has survived. Others, which fell 
into disuse, were the Maccabaean eras, dating from the 
accession of each prince, and the national era (143-142 B.C.), 
when Judaea became free under Simon. That the era 
described in Jubilees was other than hypothetical, is 
probable. Dates have also been reckoned from the fall of 
the* second Temple [Le-Horban hab-bayyith). The equation 
of the eras is as follows.: 

Year 1 after destruction = A.M. 3831 

= 383 Seleucid 
= A.D. 71 

The 'Era of Creation* is supposed to have started 
from the day of autumnal equinox of the year 3761 B.C. 
So the sun and the moon must have existed before the 
day of creation !! 


The Mohammedan calendar is purely lunar and 
has no connection with the solar year. The year 
consists of 12 lunar months, the beginning of each 
month being determined by the firtt observation of the 
crescent moon in the evening sky. The months have 
accordingly got 29 or 30 days and the year 554 or 355 
days. The new-year day of the Mohammedan calendar 
thus retrogrades through the seasons and completes 
the cycle in a period of about 32-J solar years. 

The era of the Mohammedan calendar, viz., the 
Hejira (A.H.), which was probably introduced by the 
Caliph Umar about 638-639 A.D., started from the 
evening of 622 A.D., July 15, Thursday*, when the 
crescent moon of the first month Muharram of 
the Mohammedan calendar was first visible. This 
was the new-year day preceding the emigration 
of Muhammad from Mecca which took place about 
Sept. 20 (8 Rabi I), 622 A D. 

*As the. day of the Islamic calendar commences from 4unset r 
Friday started from the evening of that day. 

C. B.-31 



For astronomical and chronological purposes the 
lengths of the months are however fixed by rule and 
not by observation. The lengths of the months in days 
for this purpose are as follows : 





Rabi-ul awwal 


Rabi-us sani 


Jamada'L awwal 


Jamada-s sani 













29 (or 30) 

The leap-year, in which Zilhijja has one day more, 
contains 355 days and is known as Kabishah, In a cycle 
of 30 years, there are 19 common years of 354 days and 
11 leap-years of 355 days. Thus 360 lunations are made 
equivalent to 10,631 days or only '012 days less than 
its actual duration. The rule for determining the leap- 
year of this fixed calendar is that, if after dividing the 
Hejira year by 30, the remainder is 2, 5, 7, 10, 13, 16, 
18, 21, 24, 26 or 29, then it is a leap-year. 

The only purely lunar calendar is the 'Islamic 
calendar', which has been in vogue amongst the 
followers of Islam since the death of the Prophet 
Muhammad (632 A.D.). But it is well-known that 
before this period Mecca observed some kind of luni- 
solar calendar in common with all countries of the 
Near East. The common story is that when pilgrims 
from distant countries and other parts of Arabia came 
to perform Hajj at Mecca (Hajj is a pre-Islamic 
practice), they often found that it was an intercalary 
month according to Meccan calculation, when no 
religious festival could be performed, and had to wait 
for a month before they were allowed to perform the 
rites. This meant great hardships for distant visitors 
and to prevent recurrence of such incidents the 
Prophet forbad^ the use of intercalary or 13th month 
and decreed that the calendar should henceforth be 
purely lunar. 

It has now been shown by Dr. Hashim Amir Ali of 
the Osmania University, Hyderabad, that the Moha- 
mmedan calendar was originally luni-solar in which 
intercalation was made when necessary, and not 
purely lunar. This view-point has now been strongly 
supported by Mohammed Ajmal Khan of the Ministry 
of Education, Govt, of India. They emphasize that 
upto the last year of the life of Mohammed, i.e., upto 
A.H. 10 or A.D. 632, a thirteenth month was inter- 
calated when necessary. The Arabs, among whom 
there were relatively few men conversant with astro- 
nomical calculations^ had a system in which a family 
of astronomers, known as Qalammas was responsible 
for proclaiming at the Hajj (falling in the last month 
of the year : Zilhijja) that a thirteenth month would or 
would not be added. Astronomically such intercala- 
tion should be made 3 times in 8 years or 7 times in 19 
years. The elder of the Qalamma had a certain amount 
of discretion in determining when this intercalation 
was to be practised, and this very practice afterwards 
caused great confusion. 

According to this view, proper intercalation was 
applied in all the years where necessary upto A.H. 10 
and consequently the year A.H. 11 (coming next, to 
the Hajj of A.H. 10) which started on March 29, 632 
A.D. {i.e., after the vernal equinox day) seems to have 
been a rather normal year, and as such all the previous 
new-year days appear to have been celebrated on the 
visibility of the crescent moon after the vernal equinox 
day. The Muslim months should accordingly occupy 
permanent places in the seasons as follows* ; — 

Muharram... Mar. — April Rajab ...Sept— Oct- 

Safar April— May Shaban ...Oct.— Nov. 

Rabi I ... May — June Ramadan . . Nov. — Dec. 

Rabi II ... June —July Shawal ...Dec. — Jan. 

Jamadi I ... July —Aug. Zilkada . . Jan. —Feb. 

Jamadi II ... Aug.— Sept. Zilhijja ...Feb. —Mar. 

~^Mi this view is accepted, it would then be necessary to shift the 
starting epoch of the Hejira era, which is commonly accepted as July 
16, 622 A.D., to an earlier date, as 4 intercalary months or 118 days 
will then have to be inserted between the new-year days of A.H. 1 and 
of A.H. 11, which is March 29, 632 A.D. The initial epoch of the 
Hejira era thus arrived at is the evening of March 19, 622 A.D., 
Friday, the day following the vernal equinox. 


Calendaric Astronomy 


The scheme of lunar months given in Table No* 4 
in a nineteen-year period, which came into vogue in 
Babylon about 383 B.C. did not however, completely 
satisfy the needs of the Babylonian calendar, because 
for religious purposes, the month was to start on the 
day the crescent moon was first visible in the western 
horizon after conjunction with the sun (the new- 

and the moon move uniformly in the same great 
circle in the heavens. But even the, most primitive 
observers could not fail to notice that neither do the 
two luminaries move in the same path, nor do they 
move uniformly, each in its own path. 

The motion of the moon amongst the stars is the 
easiest to observe. This is illustrated in the two 
figures reproduced from the Sky and Telescope, giving 

Fig. 2— Showing the positions of the sun, moon and planets among the stars in June. 1953, 
moon), a custom which is still followed in the Islamic positions of the moon, the sun, and the planets in the- 
countries. But the first visibility may not occur on field of fixed stars in the months of June and July,* 
the predicted day for manifold reasons. 1953. 

Fig. 3— Showing the positions of the sun, moon- and planets among the stars in July, j;j53. 
The table given on p. 176 is based on mean values The central horizontal line is the line of the 

Of the lengths of the year and the synodic month, celestial equator (§ 4.4), and the sinuous line represents 
which is equivalent to the assumption that the sun the ecliptic or the sun's path (§ 4.5) but we -mav 




ignore these now, and simply concentrate on the 
moon and the stars or star-clusters near which it 

The moon begins as a thin crescent on the western 
horizon on the evening of June 12, the day of the first 
visibility after the new-moon, at an angle of 11°, from 
the sun which has just set, below the bright stars 
Castor and Pollux (Punarvam). Then we notice the 
position of the moon on successive evenings at sunset. 
We find she is moving eastward at the rate of about 
13° and becoming fuller (increasing in phase). She 
passes the bright star Regulus (Magha) on the 17th, on 
the 19th, she is half and passes Leonis (Uttara 
Phalgunt) leaving it a good deal to the north. Then she 
passes the bright star Spica ( a Virginis or Citra) on the 
21st, and is then gibbous on the 23rd near the star 
a-lAbra {Vimkha). Then she passes the well known 
Scorpion-cluster and becomes full on the 27th, near 
a star-cluster which cannot be seen on the night of 
full-moon, but can be detected later as the star cluster 
Sagittarius. On the full moon day, she rises nearly 
at sunset, at 180° from the sun (opposition). On each 
successive night after full moon she rises later and 
later, and passes the phases in the reverse order, i.e., 
becomes gibbous on June 30, when she has the bright 
star Altair (Srava<na) far to the north and is half on 
July 4, and becomes a crescent on July 7 on the eastern 
sky, and then fails to appear for three days, and must 
have passed the sun on the 11th July which is the new 
moon day, when she is with the sun (Amavasya or 
conjunction, lit. the Sun and the moon living together). 
On the 12th July, she reappears on the western 
horizon as a thin crescent, near the star 8-Cancri 
{Pusyal and the cycle again starts. 

The crescent of the moon, either in the western or 
the eastern sky, is always turned away from the sun. 

The ancients must have observed the motion of the 
moon day after day, fiom new-moon to new-moon 
(a full lunation or lunar month) and become familiar 
with the stars or star-clusters which she passes. It is 
always easy to observe them when the moon is a 
crescent ; when the moon becomes fuller, the stars are 
lost in the moon's glare particularly if they are faint. 
But if observations be carried on for a number of 
years, the observers would become familiar with all 
the stars or star-clusters which the moon passes. 

By observations like this, the ancients must have 
found that both the moon and the sun are moving to 
the east, the moon very fast, the sun more slowly. By 
the time the moon, after making a whole round, comes 
back to the sun, the latter has moved further to the 
east by about 30°. For example in the above figures 
Nos. 2 and 3, the sun was somewhat to the west of the 

bright star-group Orionis iMrgosiras) to the west of 
Castor and Pollux on Jun; 11th, the day of the new- 
moon. But on the next new-moon day, July 11th, she 
has moved near Castor and Pollux (Piutarvam) about 
30° to the east. 

The ancients must have found that the moon takes 
a little over 27.3 days (sidereal period of the moon), 
to return to the same star, but to overtake the 
sun, it takes a little longer, a little over 29.5 days 
(the synodic period of the moon). Exactly i 

the mean sidereal period -27.321661 days 

=27 d 7 h 43 m 11 B .5 
with a variation of ± 3J hours 
and the mean synodic period = 29.530588 days 

= 29 d 12 h 44 m 2 fl . 
with a variation of ±7 hours. 

The Lunar Mansions : 

Many ancient nations developed the habit of 
designating the day-to-day (or night-to-night) position 
of the moon by the stars or star-clusters it passed on 
successive nights. The number of such stars or star- 
clusters was either 27 or 28 ; the ambiguity was due 
to the fact that the mean sidereal period of the moon 
is about 27 £ days, the actual period having a variation 
of seven hours, and the ancients who did not know how 
to deal with fractions, oscillated between 27 and 28. In 
India, originally there were 28 naksatras, but ultimately 
27 was accepted as the number of lunar nak?atras 
(or asterisms). 

The lunar zodiac is also found amongst the Chinese 
who designate them by the term Hsiu ; and amongst the- 
Arabs, who call them ManxiU both terms denoting man- 
sions. Both the Chinese and the Arabs had 28 mansions. 
The Indian term 'naksatra* is of uncertain etymological 
origin. Some hold that the term nafaatra carried the 
sense that 'it does not move* and meant a star. 

Names of certain 'naksatras are found in the 
oldest scriptures of India, vix., the Rg-Vedas, but a full 
list is first found in the Yajurveda (vide § 5 3). In 
the older classics of India ( the Yajurveda, the 
Mahabharatal the nak$atras invariably star/ with 
Kritiket, the Pleiades ; the supposition has been made 
that the Kfttikas were near the vernal point, when 
this enumeration was started. This is apparent from 
the couplet found in the Taittiriya Brahma<na which 
runs thus : 

Taittiriya Brahmaria, i, 1> 2, 1. 

Krttilifi svagnimadadhita 

Mukham va etannaksatranarii, Yatkrttika. 
Translation : One should consecrate the (sacred) 
fire in the Kfttikas y the Kfttikas are the mouth of 
the naksatras. 



Later during Siddhanta Jyoti$a times the enumeration 
started with Aivini (a? fcA*Mtis)>- and this is still 
reckoned to be the first of the naksairas, although the 
vernal point has now receded to the UUarabhMrapadd 
group which should accordingly he taken as the first 
naksatra. But the change has not been done because 
the Indian astrologers have failed to correct the 
calendar for the precession of equinoxes. 

The Chinese start their Hsius with Citra or 
a Virginis. This refers probably to the time when 
a Virginis was near the autumnal equinoctial point 
(285 A.D.). The Arabs start their Manxils with 
Arietis (Ash-Sharatani). 

There has been a good deal of controversy regarding 
the place of origin of the lunar zodiac. Many savants 
were inclined to ascribe the origin of the 27 nak^atra 
system to ancient Babylon, like all other early astro- 
nomical discoveries. But as far as the authors of this 
book are aware, there is no positive evidence in favour 
of this view. Thousands of clay tablets containing 
astronomical data going back to 2000 B.C., and 
extending up to the first century A D. have been 
obtained, but none of them are known to have any 
reference to 27 or 28 lunar mansions. 

On the other hand (as mentioned before) some of 
the nak§aira names are found in the oldest strata of 
the Rg-Vedas {ride § 5 2), which must be dated before 
1200 B.C., and a full list with some difference in names 
is found in the Yajur-Veda, which must be dated before 
600 B.C. Nobody has yet been able, to refute yet Max 
Muller's arguments in favour of the indigenous origin 
of the Indian nak$alra system given in his preface 
to the Rg-Veda Samhita, page xxxv. 

It should be admitted that the lunar zodiac was pre- 
scientific, i.e., it originated before astronomers became 
conscious of the celestial equator and the ecliptic, and 
began to give positions of steller bodies with these as 
reference planes. The nak$attas give very roughly 
the night-to-night position of the moon, by indicating 
its proximity to stars and star-groups. Many of the 
Indian stars identified as nak$atras are not at all near 
the ecliptic or the moon's path which, on account of 
its obliquity, is contained in a belt within ±5° of the 
ecliptic. Such are for example : 

(15) Svatu which is identified with Arcturus 
{a Booiis\. which has a latitude of 31° N. 

(22) &rava<nu, identified with a, 8, y Aquilae, having 
the latitude of 29° N. 

(23) &ravis\ha, identified with a, 0, 7l 8 Delphini, 
« having the latitude of 33° N. 

(25) Purva Bhadrapada identified with a Fegasi and 
some other adjacent stars, a Pegasi having latitude of 
19° N. 

At one time the brilliant star Vega (a Lyme) was 
also included making 28 toahsairas. But this has a 
latitude of 62° N and was later discarded. 

No satisfactory argument has been given for the 
inclusion of such distant stars in the lunar zodiac. The 
Arabs and the Chinese do not include these distant 
stars in their lunar zodiac, but fainter ones near the 
ecliptic. Prof. P. C. Sengupta is of the opinion that 
Indians generally preferred bright stars, but when such 
were not available near the ecliptic, they chose brighter 
ones away from the ecliptic, which could be obtained 
on the line joining the moon's cusps. 

The naksatras were used to name the 'days' in 
the earliest strata of Indian literature. Thus when the 
moon is expected to be found in the Magha naksaira 
(it Leonis), the day would be called the Magha day. 
This is the oldest method of designating the day, for it 
is found in the Rg-Vedas. Other methods of 
designating the day by tithis or lunar days, or by the 
seven week-days, came later. The system has continued 
to the present times. In old times, astrology was based 
almost entirely on the nak§atra$i e.g., in Asoke's records, 
the Pusya naksatra day was regarded as auspicious 
when Braltiiiavm and Sramanas were fed, in order to 
enhance the king's punya (religious merits). In the 
Mahabharaia also we find that the days are designated 
by naksatras which apparently mean the star or star- 
cluster near which the moon is expected to be seen 
during the night. 

As is apparent from Table No. 5, die naksatras dire 
at rather unequal distances, i.e., they rarely follow the 
ideal distance of 13 % \ This is rather inconvenient for 
precision time-reckoning. We find in the Vedaiiga 
Jyotisa times an attempt at a precise definition of the 
two limits of a nak$atra, which was detined as 800' 
(-13° 20') of the ecliptic. The naksaira was named 
according to the most prominent star {Yogatdra) 
contained within these limits. These are given in 
column (2) of Tabte 5. 

We do not, however, have any idea as to how the 
beginnings and endings of the naksatra divisions were 
fixed in India. The prominent ecliptic stars which were 
used as Yogatdras (junction-stars) in pre-Siddhantic 
period, are not distributed at regular intervals along 
the ecliptic ; and so it was found very difficult to 
include the stars in their respective equal divisions. 
This will be clear from table (No. 5) where the junction 
stars of the naksatras according to the Sunja- 
Siddhanta are given in col. (2). The celestial longitudes 
of the stars for 1956 A.D. are given in col. (4) and 
the beginnings- of each division for the same year are 
given in col. (5), taking the star a Virginis tc occupy 
the middle position of the naksdtra Oitrd, which marked 


Nam© of 


Purva Phalguni 
Uttara Phalguni 


Table 5.-fctar s of the Nakaafcra divisions. 
Poeitions of the Junction Stars of Naksatra lAviaiona of the Siddhantaa 

Beginning point 
of the naksatra 
division (1956) 


Junction star 





of naksatra s 





j3 Arietis 




41 Arietis 

i 1U 




7} Tauri 

1 Am 

•+■ m 


a Tauri 

^ a) 


X X 

A Orionis 



a Orionis 





j8 Geminorum 

4- A 


1 1 9 


S Cancri 

4- fi 

I u 


X -lie 


a Cancri 



1 33 



a Leonis 



1 4°, 

1 3 

8 Leonis 

I -L ^ 




(3 Leonis 


1 fi 




5 Corvi 4 J 

— 12 




a Virginis 

— 2 


on ^ 

1 4 

x *± 

a Bootis 





a Libra 





8 Scorpii 

— 1 




a Scorpii 

- 4 




\ Scorpii 





8 Sagittarii 

- 6 




o Sagittarii 

- 3 




a Aquilae 

+ 29 




)3 Delphini 

+ 31 




X Aquarii 





la a Pegasi 





la y Pegasi 

+ 12 




f Piscium 





Position of the star 
in the naksatra 




25. Purva 

26. Uttara 

27. Revati 

the position of the autumnal equinox at the time 
when the table was compiled. The figures in the last 
column represent the position of the star in the naksatra 
division of that name. It seems that a few of the 
Yogataras, viz.. No. 6 Ardra, No. 15 Srati, No. 18 
Jye$iha, No. 20 Purvasaiha, No. 21 Uttarasaolha, 
No. 22 Sravana, and No. 23 Dhanistha fall outside the 
naksatra division of which they are supposed to form the 
Yogatara. Matters do not improve much, if we shift 
the beginning of each division so as to place ( Fiscium 
(Revati) at the end of the Revati division or in 
other words at the beginning of the Asriui division. 
This will mean that the figures in col. (6) will 
then have to be increased by 3° 59', which will 
push up the Yogataras of 1 Aivini, 2 Bharani, 
3 KrtHka, 8 Pusya, 13 HaSta, 25 P. Bhadrapada, and 
26 U. Bhadrapada, so as to go outside the naksatra 
division of which they form the Yogatara. In fact no 
arrangement at any time appears to have been 
satisfactory enough for all the Yogataras to fall within 
their respective naksatra divisions. 











1 5 










1 OQ 











1 4.3 

1 5 

X 'J 







1 fi°y 




1 (33 

1 *i 






























. 55 



























The divisions of nak^atras shown in the table, as 
already stated, has been based on the assumption that 
the star Spica occupies the 180th degree of the lunar 
zodiac. This arrangement agrees with the statement 
of the Vedaitga Jyoiisa that the Dhanis\ha star 
(a or j8 Delphini) marked the beginning of the 
l)ha>«sthA division, and also of the Varaha's Surya 
Siddhanta that Regulus (x Leonis) is situated at the 6th 
degree of pe Magha division. 


The moon gains on the sun at the average rate of 
12J° per day, but it did not take the ancients long to 
discover that the daily gain of the moon on the sun 
is far from uniform ; in fact as we know now, it 
varies from approximately 10|° to 14|° per day. It was' 
therefore not possible to say beforehand whether 
the crescent moon would appear on the 29th or on the 
30th day after the beginning of the previous month. 



But the exact prediction of the day was a necessity 
from the socio-religious point of view. In India, the 
month was measured from full-moon to fMl-moon, and 
in the Mah&bharata, the great epic which was compiled 
from older materials about 400 B. C, it is recorded 
that sometimes the full moon occurred on the 
thirteenth day after the new-moon, This was taken 
to forebode great calamities for mankind. There were 
similar ideas in Babylon of which Pannekoek says : 

"When the Moon is full on the night of the 14th, the 
normal time, it was a lucky omen ; when full-moon happened 
on the night of the 13th, 15th or 16th, it wag abnormal, 
hence a bad omen. Here astrology and calendar were merged ; 
deviation in the calendar was considered an unlucky sign 
and had to be restored at the end of the month."* 

Neugebauer says : 

"The months of the Babylonian calendar are always real 
lunar months, the first day of which begins with the first 
visibility of the new crescent. The exact prediction of 
this phenomenon is the main problem of the lunar theory 
as known to us from about 250 B. C. onwards, "t 

This is rather comparatively late date. The reason 
is that the accomplishment of this objective depends 
on the evolution of methods of exact astronomical 
observations, and of a method of recording them in 
precise mathematical language. Some ancient people 
never reached this stage. As far as we are aware, 
the ancient Babylonians were the first to evolve 
methods of observational astronomy. They also arrived 
at the principles of angular measurements, found 
the apparent paths of the moon, the sun, and the 
planets in the heavens, and discovered that it was only 
the sun's path (the ecliptic) which was fixed, and the 
paths of the moon, and the planets deviated somewhat 
from it. How this was done will be related later. 

But even before these accurate methods had been 
discovered, the Babylonian astronomers had learnt a 
lot more about the moon from long period observa- 
tions. The most remarkable of these discoveries is 
that of the Chaldean Saros, or a period of 18 years 
10J days, in which the eclipses of the sun and the 
moon recur. 

The occurrence of solar or lunar eclipses, when the 
two great luminaries disappear suddenly, either partially 
or wholly, were very striking phenomena for the 
ancient and medieval people, and gave rise to gloomy 
forebodings. There were all kinds of speculations 
about the cause of the eclipses, e.g., that the sun and 
the moon were periodically devoured by demons or 
dragons. The ancient astronomers, however, found 
that a solar eclipse takes place only near conjunction 

* A. Pannekoek : The Origin of Astronomy. 

t G. Neugebauer : Babylonian Planetary Theory. 

( new r moon ), but every conjunction of trie stin and 
the moon is not the occasion for a solar eclipse. A 
lunar eclipse takes place only near opposition (full- 
moon ), but every opposition of the sun and the moon 
is not the occasion for a lunar eclipse. 

In many ancient countries, China and Babylon for 
example, records of occurrence of eclipses had been 
kept. The celebrated Greek astronomer, Ptolemy of 
Alexandria ( ca. 150 A. D. ) had before him a record 
of eclipses kept at the Babylonian archives dating 
from 747 B. C. They gave date of occurrence, time, 
and features of the eclipse, whether they were partial 
or total. From an analysis of these records, the 
Chaldean astronomers tried to discover the laws of 
periodicity of eclipses, which ultimately resulted in the 
discovery of the Saros cycle of 18 years and 10 or 11 
days. The basis of the Saros cycle is as follows : 

We do not exactly " know when the ancient 
astronomers outgrew the myth of demons periodically 
devouring the sun and the moon during eclipse times, 
and arrived at the physical explanations now known 
to every student of astronomy, and reproduced in the 
diagrams given below. 

Fig. 4— Showing an eclipse of the moon. 

But when they arrived at physical explanation of 
ellipses, they had an understanding as to why there 
are no eclipses during every full moon and new moon. 
The paths of the two luminaries must be in different 
planes. This we take up in a subsequent section more 
fully, when we describe how the sun's path or ecliptic 
was discovered. 

Suffice it to say that at some ancient epoch, some 
Chaldean astronomer discovered that the moon's path 
was different from the sun's, and therefore cuts the 
sun's path at two points, now called Nodes. The 
condition for an es&pse to happen is that the full- 
moon and new-moon must take place sufficiently close 
to the Nodes, otherwise the luminaries would be too 
far aipart, for an eajipse to take- place. - 

The 'Nodes* now take the place of the mythical dra- 
gons which were supposed to waylay the sun and the 
moon, periodically, and swallow and disgorge them. 
In Hindu astronomy, the ascending node is called 



Hcchu with the symbol arrd the descending' node is 
called' Keiu with the symbol ft, the names of the two 

month, because the nodes regress to the west. Its 
value is 27.21222 days. 




Fig. f> — Showing an annular eclipse ot the sun. 

halves of the demon, who was cut in two by gods, so 
that the sun and the moon could get out. 

In very ancient times, it was found that the two 
'Nodes' were not fixed, but moved steadily to the west, 
so that the sun took less than a year to return to the 
same node. This time is known as the * Draconitic year' 
or year of the Dragons, and its length is 346.62005 
days. The time in which the moon returns to the 
same node is known as the draconitic month or the 
month of dragons. It is slightly less than the sidereal 

Table 6. — List of Lunar 


Fig. 6— Showing a total eclipse of the sun. 

The Chaldeans appear to have found, about 400 
B. C, that 223 synodic months = 242 draconitic months. 

The reader can verify 

223 synodic month =6585.321 days 
242 draconitic months — 6585.357 days 

From their long observations of eclipses, the 
Chaldean astronomers must have found that eclipses 
recur after an interval of 6585 J days or 18 years llf 
days (or 18 years 10 J days if 5 leap-years intervene). 
This cycle has been known as the Chaldean Saros* 
The extent to which a knowledge of the cycle is useful 
is given in the following modern table. 

Eclipses of the Sa,ros cycle. 

Lunar Eclipses 

1914, Mar. 


1932, Mar. 






Part. -Total 









1916, Jan. 


1934, Jan. 















1917, Jan. 


1935, Jan. 

















1936, Jan. 







1918, June 








1919, Nov. 


1937, Nov. 







1920, May 


1938, May 















1921, Apr. 


1939, May 















1923, Mar. 


1941, Mar. 













1924, Feb. 


1942, Mar. 















1925, Feb. 


1943, Feb. 















1927, June 


1945, June 















1928, June 


1946, June 















1947, June 







1930, Apr. 


1948, Apr. 








1931, Apr. 


1949, Apr. 

















Table 7.— List of Solar Eclipses. 
Eclipses of the Saros cycle 

Solar Eclipses 

The dates of recurrence of the corresponding eclipses in three cycles from 1914 to 1967, the node at which 
the eclipse occurs, and the nature of the eclipse are shown below. 

1914, Feb. 


1932, Mar. 


1950, Mar. 












1915, Feb. 


1933, Feb. 


1951, Mar. 












1916, Feb, 


1934, Feb. 


1952, Feb. 














1935, Jan. 


1953, — 



1917, Jan. 




























1954, Jan. 




1918, June 


1936, June 














1919, May 


1937, June 


1955, June 












1920, May 


1938, May 


1956, June 



Part .-Total 









1921, Apr. 


1939, Apr. 


1957, Apr. 












1922, Mar. 


1940, Apr, 


1958, Apr. 












1923, Mar. 


1941, Mar. 


1959, Apr. 












1924, Mar. 


1942, Mar. 


1960, Mar. 



















1925, Jan. 


1943, Feb. 


1961, Feb. 












1926, Jan. 


1944, Jan. 


1962, Feb. 












1927, Jan. 


1945, Jan. 


1963, Jan. 



Ann. -Total 











1946, Jan. 


1964, Jan. 




1928, May 
























1929, May 


1947, May 


1965, May 












1930, Apr. 


1948, May 


1966, May 












1931, Apr. 


1949, Apr. 


1967, May 
















The problem of first visibility of the moon £ with the sky were discovered in ancient times. This is 
which we started cannot therefore be taken up unless taken up in the succeeding sections, 
we describe how the path of the sun and the moon in 

C. £.—32 




Observations of the positions of the sun, the moon, 
planets and stars are now made very accurately with 
elaborate instruments installed in observatories. But 
these instruments have been evolved after thousands 
of years of experience and application of human 
ingenuity, and have undergone radical changes in 
design and set-up with every great technological 
discovery. But let us see how the early astronomers 
who had no instruments or very primitive ones made 
observations, collected the fundamental data, and 
evolved the basic astronomical ideas. 

The earliest instrument used by primitive astrono- 
mers appears to have been the gnomon, which we 
now describe. 

Fig. 7— The gnomon 

The ancients determined the latitude of the place, obliquity 
of the ecliptic, the length of the year and the time of day by 
measuring the length and direction of shadow of the gnomon. 
The figure ehows the noon-shadow of the gnomon AB, AE 
being the equinoctial shaoow and AO and AD the shadow on 
two solstice-days, at a place on latitude - 0. 

Nobody can fail to see the change in direction 
and length of shadows of vertical objects throughout 
the day-time, and throughout the year. When these 
observations are carefully made, by means of the 
gnomon ( &anku in Sanskrit ), which is simply a 
vertical stick planted into the ground, and standing 
on fairly level ground of large area, without obstruc- 
tions from any direction, a good deal of astronomical 
knowledge can be easily deduced. These observations 
appear to have been made in all ancient countries. 

We have the following description, by George 
Sarton, of observations made in ancient times in 
Greece with the aid of the gnomon.* 

"It (the gnomon) is simply a stick or a pole planted 
vertically in the ground, or one might use a column built for 
that purpose or for any other ; the Egyptian obelisks would 
have been perfect gnomons if sufficiently isolated from other 
buildings. Any intelligent person, having driven his spear 

* Sarton mentions Anaximander ( c 610-545 B.C.) of Miletus as the 
earliest Ionian philosopher who used the gnomon in Greater Greece. 

into the sand, might have noticed that its shadow turned 
around during the day and that it varied in length as it 
turned. The gnomon in its simplest form was the 
systematization of that casual experiment. Instead of a 
spear, a measured stick was established solidly in a vertical 
position in the middle of a horizontal plane, well smoothed 
out and unobstructed all around in order that the shadow 
could be seen clearly from sunup to sundown. The astro- 
nomer (the systematic user of the gnomon deserves that 
name) observing the shadow throughout the year would see 
that it reached a minimum every day (real noon), and that 
minimum varied from day to day, being shortest at one time 
of the year {summer solstice) and longest six months later 
{winter solstice^. Moreover, the direction of the shadow 
turned around from West to East during each day, 
describing a fan the amplitude of which varied througout 
the year"'.* 

From the observation of the shadows cast by the 
gnomon, many useful deductions could be made. 
These are : — 

(1) Mark the points in the morning and in the 
evening when the shadows are equal in length and 
draw the lines showing the shadows. Then bisect 
the angle between the two shadow lines. This gives 
us the meridian or the north-south direction of the 

The process of bisection was done by taking a rope 
attaching extreme points to the end points of the 
equal shadows ; then take the mid-point of the rope, 
and stretch the rope, and mark the position of 
the mid-point. This connected to the pole gives us 
the meridian line. If we draw a circle, with the pole 
as centre, and draw the meridian, the point where it 
strikes the northern semi-circle is the North point, 
opposite is the South point. The East and West 
points are found by drawing a line at right angles to 
the north-south direction. 

So the cardinal directions are found. 

(2) Observe the position of the sunrise from day 
to day. If observations are carried on throughout the 
3'ear, there will be found two days in the year when 
the sun will arise exactly on the east point. Then it 
is found that the day and night are equal in length. 
These days are called the Equinoctial days. Let us 
start from the equinoctial day in Spring (vernal 
equinox). This happens on March 21st. Then we 
observe that the sun at sunrise is steadily moving to 
the north, at first rapidly, then more slowly. Near 
the extreme north, the sun's movement is very slow, 
so this point is called the 'Solstice which means the 
sun standing still. Actually the sun reaches its 
northern-most point on June 22 (summer solstice). 

* George Barton : A History of Science, p. 174. 



The day is longest on this date. Then the sun begins to 
move south till it crosses the east point on September 
23, when day and night again become equal (the autum- 
nal equinox day). It continues to move south, till 
the extreme south is reached on December 22, (the 
winter solstice day), when daylight is shortest for 
places on the northern hemisphere. Then the sun 
turns back towards the east point reaching it on 
March 21, and the year-cycle is complete. 

The gnomon thus enabled the ancient astronomers 
(in Babylon; India, Greece, and China) to determine : 

(a) The Cardinal points : Fast, North, West, and 
South ; the north-south line is the meridian line (the 
Yamyottaia-rekha in Indian astonomy). 

(b) The Cardinal days of the Year : vix., 

The Vernal Equinox (V.E.) day, when day and 
night are equal. 

The Summer Solstice (S.S.) day, when the day 
is the longest for observers on the northern hemisphere. 

The Autumnal Equinox (A.E.) day, when day 
and night are again equal. 

The Winter Solstice (W.S.) day, when the day 
is the shortest for observers on the northern hemisphere. 

All early astronomical work was done in the 
northern hemisphere. 

These methods are fully described in the Surya- 
ShWianta, Chap. Ill, but they appear to have been 
practised from far more ancient times. In the 
appendix (5-C), we have quoted passages from the 
Aitareija Brahmana which shows that the gnomon was 
used to determine the cardinal days of the year at the 
time when this ritualistic book was compiled. The 
date is at least 600 B.C., i.e., before India had the 
Greek contact. It may be considerably older even. 

(c) To mark out the Seasons : We have 
mentioned earlier that in countries other than Egypt, 
there were no impressive physical phenomenon like 
the arrival of the annual flood - of the Nile to mark 
the beginning of the solar year, or of the seasons. The 
seasons pass imperceptibly from the one to the other. 

The gnomon observations probably enabled the 
early astronomers of Babylon and Greece to define the 
onset of the seasons, and the length of the year with 
greater precision. 

In Graeco-Chaldean astronomy, we have four 
seasons : 

Spring from V.E. to S.S. 

Summer S.S. to A.E. 

Autumn*- „ A.E. to W.S. 

Winter- „ W.S. to V.E. 
Thus every season starts immediately after a 
cardinal day of t,he year and ends on the next 
cardinal day. 

According to Neugebauer : 

"Babylonian astronomy ( during Seleucid periods, 
300 B.C. -75 A.D. ) waa satisfied with an exact four-division 
of the seasons as far as solstices and equinoxes are 

concerned, with the summer solstice ( and not the vernal 

point ) as the fixed point."* 

At a later stage, they however found that the four 
seasons had unequal lengths ( vide § 3*1). 

The above definition of 'seasons' has come down 
to modern astronomy. The Hindu definition of 
seasons was different ( vide § 5-6 and 5-A ) 

The observation of the Cardinal days of the year 
appear to have been carried out all over the ancient 
world by other methods, and often in a far more 
elaborate manner. People would observe the 
day-to-day rise of the sun on the eastern horizon, and 
mark out the days when the sun was farthest north 
(summer solstice day), or farthest south (winter solstice 
day). The time period taken by the sun to pass from 
the southern solstitial point to the northern solstitial 
point was known in the Vedas as the Uttardyana 
(northern passage), and that taken by the sun to pass 
from the northern solstitial point to the southern 
solstitial point was known as the Daksinayana 
(southern passage). Exactly midway between these 
points the sun rises on the vernal and autumnal 
equinoctial days. From the passage in the fcatapatha 
Brahma^ quoted later ( vide §53), we see clearly that 
the point on the eastern horizon, where the sun rose 
on these days, was recognized to be the true east. 

Doubt has been expressed about the ability of 
Vedic Aryans to make these * observations, but to these 
objections, B. G. Tilak replied in his Orion, pp. 16-17. 

"Prof. Weber and Dr. Schrader appear to doubt the 
conclusion on the sole ground that we cannot suppose the 
primitive Aryans to have so far advanced in civilization 
as to correctly comprehend such problems. This means 
that we must refuse to draw legitimate inferences from 
plain facts when such inferences conflict with our precon- 
ceived notions about the primitive Aryan civilization. I 
am not disposed to follow this method, nor do I think that 
people, who knew and worked in metals, made clothing 
of wool, constructed boats, built houses and chariots, 
performed sacrifices, and had made some advance in 
agriculture, were incapable of ascertaining the solar 
and the lunar years. They could not have determined it 
correct to a fraction of a second as modern astronomers 
have done ; but a rough practical estimate was, certainly, 
not beyond their powers of comprehension. * 

The best example of the ability of the ancient 
people to observe the cardinal points of the sun's 
motion is afforded by the Stonehenge in the Salisbury 
plains of England, of which detailed accounts 

* Neugebauer : Babylonian Planetary Theory, Proc. Amer. Philoa. 
Soc. Vol. 98 : 1, 1954, p. 64. 



have recently appeared in Scientific American ( 188, 
6-25, 1953 ) and Discovery (1953, Vol. XIV, p.276). 

It is related in these two publications, that not a 
long time subsequent to 1800 B.C., say about 1500-1200 
B.C., the then inhabitants of Britain, who had not even 
learnt the use of any metal, but used only stone 
implements, could construct a huge circular area 
enclosed by large upright monoliths forming lintels 
and with a horse-shoe shaped central area having its 
axis in the direction of sunrise on the summer solstice 
day. It has been proved, almost beyond any doubt, 
that the Stonehenge was used for the ceremonial 
observation of sunrise on this day. Sir Norman 
Lockyer in 1900 found that the direction of the axis of 
the horse-shoe actually makes an angle of about H° with 
the present direction of sunrise on the summer solstice 
day. He did hot think that it was a mistake on the 
part of the original builders ; but that on account 
of the change in obliquity (angle between equator and 
ecliptic), the present direction of sunrise had changed 
to the extent of H° and using the rate of change of 
obliquity, he could fix up the time of construction at 
1800 ± 200 B.C. This estimate has been brilliantly 
confirmed by C 14 -analysis of some wood charcoal 
found in the local burial pits which are presumed to be 
contemporary with the erection of the Stonehenge. 

After this brilliant confirmation of Lockyer's 
hypothesis, it is hoped that there will be less hesitation 
on the part of scholars to admit that it was possible 
for the Vedic Aryans who knew the use of metal and 
were far more advanced than the stone-age people of 
Britain, to devise methods for the observation of the 
cardinal points of the year. 

How did they observe these points ? Probably in the 
same way as the Britishers of 1500 B.C., by observing 
from a central place, the directions of sunrise on the 
eastern horizon throughout the year. The directions 
of the solstitial rises could be easily marked. Probably 
the equinoctial points were found by bisecting the 
angle between these two directions by means of ropes 
as described in the Sulva- Sutras. 


Almost all ancient nations were familiar with the 
night-sky either as shepherds, travellers or navigators, 
and were acquainted with more detailed knowledge 
of the revolving blue firmament studded with stars 
than the modern city dweller. The striking constell- 
tions like the Great.Bear, the Pleiades, the Orion could 
not but catch their fancy and references to these star- 
groups arc found in ancient literature, in the Vedas, m 

the book of Job (the Bible) and in Homer. In the last, 
the star-groups are used by sailors to find out their 
orientation. Representations of star-groups are found 
in ancient Babylonian boundary stones of about 
1300 B.C. (see Fig. 15). 

Let us now see how these observations were 

Suppose, on a clear moonless evening in early 
Spring (say March ) and at about 8-30 P.M., we take 
our stand in a wide field undisturbed by city lights, 



Fig. 8-Showing the positions of Ursa Major ( at 
interval of 3 hours. 

and our vision is unobstructed in all directions. We 
now face the north. We shall find the appearance 
of the heavens as shown in Fig. (8) : 

In the north, a little high up to our right hand 
side we cannot fail to observe the conspicuous 
constellation of seven stars, called in Europe the 
Great Bear, but in India, the Saptanti or seven seers. 
If we observe the heavens 3 hours later, we shall 
observe that the group has changed its position as 
shown in Fig. (8). Let us fix our attention on the 
two front stars (the pointers) of the Great Bear 
and join a line through them. The line joining these 
two stars appear to behave like the hands of a watch, 
for if produced they pass through a star half as bright 
at some distance, and appear to have revolved about it 
as centre. This star is called the Pole Star or Polans, 
or Dhruva in Sanskrit which means fixed. If we 
observe throughout the night, we shall find that the 
Polaris remains approximately fixed, and the line of 
pointers continues to go round it. The next day, at 



8-26 P.M., nearly 24 hours later they are again almost 
exactly at the same position. 

We naturally come to the conclusion that the 
whole starry heavens have been rotating round an 
axis passing through the observer and the Pole Star 
from east to west, and the rotation is completed in 
nearly 24 hours (exactly 23 h 56 m 4 8 of mean solar time). 

Definition of the Poles 

The celestial poles, or the poles round which 
the rotation of the celestial sphere takes place may . 
therefore be defined as those two points in the sky 
where a star would have no diurnal motion. The 
exact position of either pole may be determined with 
proper instruments by finding the centre of the small 
diurnal circle described by some star near it, as for 
instance, the stars belonging to the Ursa Minor group. 
Actually the so-called pole star is at present 57 
minutes away from the correct position of the pole 
which is not actually occupied by any star. 

Since the two poles are diametrically opposite in 
the sky; only one of them is usually visible from a 
given place : observers north of the equator see only 
the north pole, and vice versa in the southern 
hemisphere. The south pole is not marked by any 
prominent star. 

Knowing as we now do, that the apparent revolu- 
tion of the celestial sphere is due to the rotation of 
the earth on its axis, we may also define the poles as 
the two points where the earth's axis of rotation (or 
any set of lines parallel to it), produced indefinitely, 
would pierce the celestial sphere. 

The Celestial Equator and Hour Circles 

The celestial equator is the great circle of the 
celestial sphere, drawn halfway between the poles 

Z R 

Fig. 9— The celestial sphere. 

(and therefore everywhere 90° from each of them), and 
is the great circle in which the plane of the earth's 
equator cuts the celestial sphere, as illustrated in 
Fig, (9). Small circles drawn parallel to the celestial 

equator, like the parallels of latitude on the earth, 
are called parallels of declination. A star's parallel of 
declination is identical with its diurnal circle. 

The great circles of the celestial sphere, which pass 
through the poles in the same way as the meridians on 
the earth, and which are therefore perpendicular to 
the celestial equator, are called hour-circles. Each 
star has its own hour-circle, which at the moment 
when the star passss the north-south line through the 
zenith of the observer, coincides with the celestial 
meridian of the place. 


The apparent path of the sun in the sky is known 
in astronomical language as the ecliptic. It is a great 
circle cutting the celestial equator at an angle of ca 
23J° (exactly 23° 26' 43" in 1955, but the angle varies 
from 22° 35' to 24° 13'). This is known as the 
obliquity of the ecliptic. 

The ecliptic is the most important reference circle 
in the heavens, and let us see how a knowledge of it 
was obtained in ancient times. 

It is obvious that a knowledge of the stars marking 
the sun's path could not be obtained directly as in the 
case of the moon ; for when the sun is up, not even 
the brightest stars are visible. The knowledge must 
have been obtained indirectly. Early observers were 
accustomed to observe the heliacal rising of stars, i.e., 
observe the brilliant stars lying close to the sun which 
are on the horizon just before sunrise. This must 
have given them a rough idea of the stars lying close to 
the sun's path. From these observations, as well as 
from successive appearances of the moon on the first 
days of the month as narrated in § 41, they must have 
also deduced that the sun was slipping from the west 
to the east with reference to the fixed stars, and 
completing a revolution in one year. But how ivas 
this path rigorously fixed ? 

It appears that a knowledge of the stars lying on, 
or close to the moon's path was obtained from observa- 
tions made during lunar, rarely of solar eclipses. 

They must have realized, as narrated in § 4.2, 
that during a total lunar eclipse, the moon occupies a 
position in the heavens opposite the sun, and the stars 
close to the moon, which become visible during 
totality, approximately mark out points on the sun's 
path. So the word * Ecliptic* which means the locus of 
eclipsas, came to denote the sun's path. 

The two points of intersection of the ecliptic 
with the celestial equator are called respectively the 



Firsi point of Aries, and the First point of Libra. The 
first point of Aries is the ascending node, when the 
sun passes from the south to the north > the first 
point of Libra is the descending node, when the sun 
passes from the north to the south. We have vernal 
equinox when the sun is at the first point of Aries, 
summer solstice when the sun is at the first point of 
Cancer, autumnal equinox when the sun is at the first 
point of Libra, and winter solstice when the sun is 
at the first point of Capricorn. To the origin of 
nomenclature, we return later. 

The celestial equator and the ecliptic are the most 
important reference planes in astronomy. The 
positions of all heavenly bodies are given in terms of 
these planes, taking the first point of Aries as the 
initial point. We explain below the scientific defini- 
tions of spherical co-ordinates used to denote the 
position of a body on the celestial globe. 

Fig. 10.— Stowing the spherical co-ordinates of a «ar. 

In this figure : 

P= Celestial pole (dhnud). 
rQi. =• Celestial equator. 

K>Pole of the ecliptic (kadamba). 
X s = Plane of the ecliptic. 
T = First point of Aries (vernal equinox), 
s = First point of Cancer ( summer solstice). 
^ = First point of Libra (autumnal equinox). 
Vf «= First point of Capricorn (winter solstice). 
S = A heavenly body. 
PS^=Great circle thro'P,S cutting equator at Q. 
rQ^Right ascension — a 
QS« Declination *S 

KS^ Great circle through K, S cutting ecliptic 
at C. 

rC« Celestial longitude « X 
CS ~ Celestial latitude = p 
Let PS cut the ecliptic at B. Then 
rB K Polar longitude or dhruvaka = I 
BS=* Polar latitude or vik$epa=*d 
These last two peculiar co-ordinates, now no longer 
used, were used by the Surya Siddhanta to denote star 
positions. They have been traced by Neugebauer to 
Hipparchos five centuries earlier. 

The position of a stellar body may be defined by 
either its right ascension (a) and declination (8), 
or its celestial longitude(x) and latitude(0). 
The positions of stars in these co-ordinates began to 
be given from the time of Claudius Ptolemy (150 A.D.) 
who used them in his Syntaxis. 


The early astronomers must have found that the 
sun's path in the heavens was almost fixed, while 
that of the moon, and of the planets, which acquired 
for astrological reasons great importance from about 
1200 B.C., strayed some degrees to the north and south 
of the ecliptic. 

In case of the moon the deviation from the ecliptic 
was found to be not much greater than 5°, but some 
of the planets strayed much more; in. the case of 
Venus, her perpendicular distance from the ecliptic 
rises sometimes as high as 8° degrees. So a belt was 
imagined straying about 9° north and 9° south of the 
ecliptic, in which the planets would always remain in 
course of their movement. This belt came to be 
known as the 'Zodiac* 

The complete cycle of this belt was divided into 12 
equal sectors each of 30°, and each sector called a 
'Sign'. The signs started with one of the points of 
intersection of the ecliptic and the equator, and the 
first sign was called " Aries* after the constellation of 
stars within it. The names of the succeeding signs are 
given in Table No. 8 on the next page, in which : 

The first column gives the beginning and ending of 
the signs, the vernal equinoctial point being taken as 
the origin. r 

The second column gives the international names 
which are in Latin with the symbols used to denote 
the signs. 

The third column gives their English equivalent. 

The fourth column gives the Greek names. They 
are synonimous with the international names. 

The fifth column gives a set of alternative name* 
for the signs given by Vartthamihira. 



Table 8 —Zodiacal Signs. 
Different Names of Zodiacal Signs 

Beginning and Name of the English Greek 

ending of the Signs & equivalent names 

Signs Symbol 

(1) (2) (3) (4) 

0°- 30° T Aries Bam Ki-ios 

30 - 60 B Taurus Bull Tauros 

60 - 90 n Gemini Twins Didumoi 

90 -120 s Cancer Crab Karxino; 

120 -150 Q. Leo Lion Leon 

150 -180 11 JP Virgo Virgin Parfchenosj 

180 -210 . ■ ^ Libra Balance Zugos 

210 -240 i'l Scorpio Scorpion Scorpios 

240 -270 t Sagittarius Archer Tozeutes 

270 -300 V/ Capricornus Goat Ligoxeros 

300 -330 - Aquarius Water Bearer Gdroxoos 

330 -360 K Pisces Fish Ichthues 

The sixth column gives the Indian names. 
The seventh column gives the Babylonian names. 
It can be easily inferred from the table that the 
names are of Babylonian origin, but their exact 
significance is not always known. It has been assumed 
that the symbols used to denote the signs have been 
devised from a representation of the figure of the 
animal or object after which the sign has been named, 
for example, the mouth and horns of the Ram, the same 
of the Bull, and so on. 

It is seen that Varahamihira's alternative names 
given in column ( 5 ) are simply the Greek names 
corrupted in course of transmission and as adopted for 
Sanskrit ; with the exception of the name for 
Scorpion, which is given as l Kaurpa". This has phonetic 
analogy' with the corresponding Babylonian sign name 
Akrabu for Scorpion. The purely Sanskrit names 
given in column (6) are all translations of Greek names 
with the exceptions of : 

(3) Twins, which become Miihuna or Amorous 

(9) the Archer, which becomes the 'Bow', 

(10) the Goat, which becomes the 'Crocodile', 

(11) Water bearer, which becomes the 1 Waterpot'. 
Some of them appear to have been translations of 
Babylonian names. 

The Babylonian names, as interpreted by Ginzel* 
are given in the seventh column, with their meanings. 

It is thus seen that the names of the zodiacal signs 
are originally of Babylonian origin. They were taken 
over almost without change by the Greeks, and 
subsequently by the Romans, and the Hindus, from 
<Graeco-Chaldean astrology. 
* Giazdi Handbuch der Mathematischen- unci Technischm Chrono- 
loati. Vol. I, P, 84. 





Kuli r a 





Tanks ika 









Karka or Karkata 

Sim ha 










Ku or Iku (Earn) 
Te-te (Bull) 
Masmasu (Tsvins) 
Nangaru (Crab) 
Aru (Lion) 
Ki (Virgin) 
Nuru (Scales) 
Akrabu (Scorpion) 
Pa (Archer) 
Sahu (Goat) 
Gu (Water carrier) 
Zib (Fish) 

But why was such an odd 
names chossn for the 'Signs' 
interesting speculations. The 

assortment of animal 
? There have been 
reader may consult 
Brown's Researches into the Origin of Ike Primitive 
Constellations of the Greeks, Phoenicians and Babylonians, 
London, 1900. 

These signs were taken up by almost all nations in 
the centuries before the Christian era on account of 
the significance attached to them by astrologers. In 
Greece, they were first supposed to have been 
introduced by the early Greek astronomer Cleostratos, 
an astronomer who observed about 532 B.C. in the 
island of Tenedos off the Hellespont who introduced 
the designation 'Zodiac* to describe the belt of stars 
about the ecliptic. The twelve 'Zodical Signs' are 
not known in older ritualistic Indian literature like 
the Brahmanas. They appear to have come to India 
in the wake cf the Macedonian Greeks or of nations 
like the Sakas who were intermediaries for trans- 
mission of Greek culture to India. 

Confusion in the starting point of the Zodiac 

The Initial Point' of the zodiac should be the 
Vernal Point or the point of intersection-of the ecliptic 
and the equator, but as will be shown in the next 
section, this point is not fixed, but moves west-ward 
along the ecliptic at the rate of approximately 50- per 
year (precession o£ the equinoxes). This motion is 
unidirectional, but bsfore Newton proved it to be so in 
1687 from dynamics and the law of gravitation, there 
was no unanimity even among&t genuine astronomers 
about the uni-directional nature of precessional 
motion, inspite of overwhelming observational 



The hesitation of the medieval astronomers in 
accepting precession can be easily understood. Most 
of them earned their livelihood by practising the 
'Astrological Cult' which was reared on the basis that 
the signs of the zodiac are fixed, and coincident with 
certain star-groups ; but this assumption crumbles to 
the ground if precession is accepted. But as historical 
records now show, though astronomers had clearly 
recognized that the initial point should be the point 
of intersection of the equator and the ecliptic, there 
was no unanimity even amongst ancient astronomers 
of different ages regarding the location of this 
point in the heavens, because it was not occupied by 
any prominent star at any epoch and the ancients 
were unaware of the importance of its motion 
(vide § 4-9). 


We have seen that it was the needs of the 
calendar which gave rise to scientific astronomy— 
which in the earliest times covered : 

.MOV. 24 

The attention of mankind was drawn in remote 
antiquity to the five star-like bodies : 

Venus, Jupiter, Mars, Saturn and Mercury. 

Venus and Jupiter and occasionally Mars are more 
brilliant than ordinary stars. Sooner or later it was 
found that while the ordinary stars remain fixed on 
the revolving heavens these five stars creep along 
them, as a modern author puts it, 'like gloio-ivorms 
on a ivhirling globe', each in its own way. Venus 
appears as a morning and evening star, the maximum 
elongation being 47°. It early drew the attention of 
'sea-faring people, its appearance on the eastern horizon 
indicating early sunrise to persons on lonely seas. 
But it took mankind some time to discover that it was 
the same luminary which appeared for some period as 
a morning star, then as an evening star. Its brilliance 
could not but strike the imagination of mankind. 
Mercury also appears regularly as morning and evening 
star, and it must have been discovered later than 
Venus, but still at such a remote age in antiquity that 
all traces of its discovery are lost. 

The motion of the brilliant luminary, Jupiter 
across the sky attracted early attention ; Mars 

MAR. £4 

The Path of Mart Among the Stars in 1939. 

Fig. 11— Showing the retrograde motion of Mars. 
Although the planets always move in the same direction round the suti, their: apparent motion among 
the fixed stars as seen from the earth, is not always in the same forward direction. They sometimes 
appear to move also in the backward direction among the stars, and this is known as the retrograde 
motion of a planet. The above figure reproduced from Pictorial Astronomy by Alter and Cleminshaw 
illustrates how Mars was seen to retrograde during June 24 to August 24. 

(a) Systematic observation of the movements of 
the moon, and the sun, 

(b) Recording of the observations in some 
convenient form on permanent materials, 

(c) Invention of mathematical methods to deal 
with the observations, with a view to predict 
astronomical events. 

It is not, however, correct to say that it was the 
calendar based on the sun and the moon which 
provided tfae sole stimulus for astronomical studies. 
fa one t&ftft, "the planets strongly captured the attention 


/ A. Pjg$#<^C0ek : Origin of Astronomy, p. 351. 

occasionally bursts into brilliance with fierce, red 
light, which could not but attract notice. The three 
planets, Mars, Jupiter, and Saturn though generally 
moving to the east, from time to time reverse their 
direction of motion (retrograde motion), as shown 
in Fig. 11. 

From very early times and amongst widely 
separated communities, mystifcal importance was 
ascribed to the wandering of the Janets. 

These mystical ideas took & very definite form in 
the shape of 'Planetar^ AslroUW which grew in 
Mesopotamia dUring the period B.C. to 800 B.C. 
This Planetary Astrology i* *» m distinguished from 



an older form of Astrology widely found in Vedic 
India, which centred mainly round the moon, and the 
lunar mansions, and to a lesser extent on the sun. 
The conjunction of the moon with certain nak$atras 
was considered lucky, others unlucky (vide § 4'1). 

Planetary Astrology took the world by the 
storm after 300 B.C. and its influence was strongest 
during middle ages in Europe, till the rise of 
rationalism and modern science almost completely 
undermined this influence. But it still survives amongst 
the credulous in the West, but to a far greater extent 
than amongst the eastern nations. 

emerged in Babylonian history from the time of 
Assyrian supremacy (ca. 1300 B.C.), for these appeared 
to be linked up with the mysteries of Heaven itself, 
and the astrologer enjoyed very great prestige amongst 
the public, for did he not possess the mysterious power 
of foretelling correctly the dates of eclipses ! 

Here are some of the samples o£ astronomical 
omina during the last centuries of Assyrian power 
(900 B.C.-600 B.C.). 

"Mercury went back as far as the Pleiades' 1 ; "Jupiter 
enters Cancer" ; "Venus appears in the East" ; "Mars is 
very bright" ; "Jupiter appears in the region of Orion" ; 


Fig. 12— Showing the motion of Mars relative to the earth. 

By placing the sun at the centre and having the earth and the other planets revolve in circles around 
it Copernicus (1473-1543) was able to explain the backward motion of the planets among the stars much 
more simply than in the Ptolemaic system. This is illustrated in the above figure, taken from Phonal 
Astronomy, in the case of Mars as seen from the earth. The earth's speed is IB* miles a second while that 
of Mars is onlv 15 miles a second. As the earth overtakes Mars, the latter seems to move backward The 
direct motion of Mars to the east is shown at positions 1, 2 and 3, backward or retrograde motion to the 
west at 4 and 5, and direct motion to the east again at 6 and 7. 

What was the reason for the strong fascination 
which man has for astrology ? 

Mankind has always a psychological weakness 
for omina, i.e., some signs which can predict future 
events, good or bad. The older form of omina 
were rather crude, viz., flight of certain birds like the 
crow, or movements of animals like the jackal or the 
snake, howlings of certain birds and animals. In many 
countries, sheep and goats were sacrificed to gods on 
the eve of great enterprises, and Augurs claimed to 
be able to interpret the intentions of the gods 
from an examination of lines and convolutions on 
the liver of the sacrificial animal ( fiepatoscopy ). 
Meteorological phenomena such as a lightning 
discharge, haloes round the moon, aurora were also 
regardefas 'omens'. 

The older forms of omina were all apparently very 
crude compared to planetary omina which gradually 

"Mars stands in Scorpio, turns and goes forth with 
diminished brilliancy" ; "Saturn has appeared in the Lion" ; 
"Mars approached Jupiter" ; and so on. 

There is not a trace of scientific interest in these texts ; 
the mind of the reporters is entirely occupied by the omens : 
When such or such happens, 

"it is lucky for the king, my lord" ; 

or, "copious floods will come" ; 

"there will be devastation" ; 

"the crops will be diminished" ; 

"the king will be besieged" ; 

"the enemy will be slain" ; 

"there will be raging of lions and wolves" ; 

"the gods intend Akkad for happiness" ; 

and so on. 

Yet, with all those observations, these reports represent 
a considerable astronomical activity. For the first time 
in history a large number of data on the planets had been 

C.R.— 33 



collected ; it implies a detailed knowledge of facts about 
their motion."* 

The huge temples, called Ziggurats, ruins of which 
have been found in Mesopotamia, are supposed to have 
been dedicated to the planetary gods, each storey being 
assigned to a particular god. It was the duty of temple 
priests to keep the planets under observation, and 
record their positions on the only writing material 
available then viz* clay-tablets. Hundreds of thousands 
such clay tablets have been discovered in the ruins of 
Ziggurats, royal palaces and libraries, and patiently 
interpreted by western scholars like Kugler. 

the moon, and the planets, and compilation of tables 
of positions, which afforded the basis on which modern 
astronomy has been built up. In the large number of 
ancient horoscopes which have been studied by 
scholars, and in the astronomical tables compiled by 
ancient and medieval scholars, we have a huge 
amount of data on planets. 
Pannekoek observes : 

"The circumstance that made this possible for astro- 
nomy was the occurrence of extremely simple and striking 
periodicities in the celestial phenomena. What looked 
irregular on occasional and superficial observing revealed 

its regularity in a 

Fig. 13— Ziggurat. 

(Reproduced from Zinner's Gesckichte der Hternkunde) 

At first, planetary astrology appear to have baen 
confined to states, and kings or powerful officials 
representing the state. But after the conquest of 
Babylon by the Persian conqueror Cyrus (538 B.C.), 
they appear to have been extended to private 
individuals. Thus came into existence 'Horoscopic 
Astrology', in which a chart is made of the 12 signs 
of the zodiac with the position of the planets shown 
therein, for the time of his birth, from which are 
foretold the events of his life and career. We are 
not interested in 'Horoscopic Astrology' at all, but 
wish only to remark that but for the stimulus provided 
by astrology, there would not have been that intense 
activity during ancient and (from about 500 B.C.) 
medieval times, for large scale observations of the sun, 


abundance of data. 


* Pannekoek : The Origin of Astronomy— reprinted from the 
; Monthly Notices of the Royal Astronomical Society, Vol III, 
No. 4, 1951, pp. 351-52. 

Fig. 14— Showing a horoscope cast in the European method. 
The:£sign Aries, the first house or ascendant, is in the east. 
The sign Capricornus, the 10th house, is on the meridian at the 
time of birth and so is in the south. The planets occupying 
the different signs are shown by the respective symbols. 



Regularities were not sought for ; but regularities imposed 
themselves, without giving surprise. They aroused certain 
expectations. Expectation is the first unconscious form of 
generalized knowledge, like all technical knowledge in daily 
life growing out of practical experience. Then gradually the 
expectation develops into prediction, an indication that the 
rule, the regularity, has entered consciousness. In the 
celestial phenomena the regularities appear as fixed periods, 
after which the same aspects return. Knowledge of the 
periods was the first form of astronomical theory". * 

The astronomical knowledge which the Chaldean 
astronomers bequeathed to the world are : 

(1) Conception of the celestial equator and 
racognition of the ecliptic as the sun's path. 

(2) A number of relations between the synodic 
and other periods of the moon and planets, vix., 

1 year = 12.36914 lunar months ; 

modern value = 12.36827 lunar months. 

Mean daily motion of the sun — 59' 9" ; 
modern value = 59' 8'\3. 

Mean daily motion of the moon -=13° 10' 35" ; 
modern value = 13° 10' 35".0 

Extreme values of the true motion of the moon : 
15° 14' 35" to. IF 6' 35 . 

According to modern determination these limits 
are about 15° 23' to 11° 46'. 

Length of the anomalistic month — 27.55555 days ; 
modern value = 27.55455 days. 

Or 9 anomalistic months = 248 days ; 
modern value = 247.991 days. 

Length of the synodic month = 29.530594 days ; 
modern value = 29.530588 days. 

223 synodic months = 242 draconitic months. 

This gave rise to the Chaldean Saros cycle 
of eclipses. 

269 anomalistic months = 251 synodic months. 
The length of the anomalistic month 
deduced from this relation = 27.554569 days, 
the modern value being .27.554550 days. 

The Greek papyri gives longitudes of the moon for 
dates 248 days apart. This period is based on the 
Babylonian relation : 9 anomalistic months = 248 days. 
After eleven such steps of 248 days, there is a big step 
of 303 days in the ephemeris. The length of the 
anomalistic month derived from these steps are as 

*Pannekoek : The Origin of Astronomy, p. 352. 

No. of anomalistic No. of Length of the 

months days anomalistic month 


D 9 248 27.555,556 days 

A 11 303 27.545,455 

C-11D+ A... 110- 3031 27.554,545 
Actual value = 27.554,550 

It is not sure whether these figures were arrived at 
by the Babylonians or by astronomers of other places. 
But these and the more accurate approximation of the 
moon's motion is found in the Paftca Siddhantika of 
Varahamihira and is found used by Tamil astronomers. 

In the Paftca Siddhantika the synodic revolutions of 
planets are given, but they apparently differ much 
from the actual figures. The figures are quoted in 
col. (2) of the table No. 9 below. The actual periods of 
the synodic revolutions in days are given in col. (3). 

Tahle 9. — Synodic revolutions 
of planets from Panca-SiddhnntikiL 

Planet As given Actual Converted from 

in P.S. (days) Col. (2) 


(1) (2) (3) (4) 

Mars 768f 779.936 779.944 

Mercury 114A 115.878 115.870 

Jupiter 393£ 398.884 398.868 

Venus 575| 583.921 583.880 

Saturn 372| 378.092 378.093 

Dr. Thibaut in his Paftca Siddhantika could not 
explain the figures in col. (2). It can be verified that 
we can obtain the figures in col. (3) if we multiply the 
corresponding figures in col. (2) by 

365.2422 u ^ , 5.2422, 
360 ° r by + - 360 > 

The figures obtained by such multiplication are 
shown in col. (4), which are found to be very close 
to the fgures in col. (3). The figures in col. (2) can be 
explained in another way, vi%., they are in degrees 
representing the arc through which the sun moves 
between two conjunctions. In other words, the 
figures in col. (2), not being ordinary mean solar days, 
are 'saura days* of Indian astronomy, a snxra day 
being the time taken by the sun to move through one 
degree by mean motion, or 360 saura days = 365.2422 
mean solar days. This explanation has been found by 
O. Neugebauer (ride his Exact Sciences in Antiquity). 
Most of these data were known to Hipparchos and also 
to Geminus, a Greek astronomer, who flourished about 
70 B.C. 

The "astronomical science'' as evolved by the 
Chaldean astronomers, is seen to be in reality the by- 



product of the huge amount of astrological nonsense, 
a few pearls in a huge mass of dung, as Alberuni 
observed nearly ten centuries ago. Let us see when 
these "pearls" gradually crystallized out of the 

Two texts called 'Mul Afiri dated round about 
700 B.C. have been discovered which contain summary 
of the astronomical knowledge of the time. Here is 
one of the pertinent passages from Neugebauer's 
Exact Sciences in Antiquity (p. 96). 

They *re undoubtedly based on older material. They 
contain a summary of the astronomical knowledge of their 
time. The first tablet is mostly concerned with the fixed 
stars which are arranged in three "roads", the middle 
one being an equatorial belt of about 30° width. The 
second tablet concerns the planets, the moon, the seasons, 
lengths of shadow, and related problems. These texts are 
incompletely published and even the published parts are 
full of difficulties in detail- So much, however, is clear : 
we find here a discussion of elementary astronomical 
concepts, still quite descriptive in character but on a purely 
rational basis. The data on risings and settings, though 
still in a rather schematic form, are our main basis for 
the identification of the Babylonian constellations." 

The passage indicates that the Chaldean astro- 
nomers of this period could locate the north pole, and 
had come to an idea of the celestial equator, and could 

cuts the horizon at the east and west points as deter- 
mined by the gnomon. 

The Ecliptic :_From archaeological records, it is 
generally held that a knowledge of the star-groups lying 

Fig. 15— Two sculptured stones of ancient Babylon displaying the 
Sun, the Moon, Venus and Scorpion— symbols of a primitive astro- 
logical science which fathered the modern conception of astronomy. 

close to the ecliptic was obtained in Babylon as early as 

Rg. J&— Babylonian Boundary Btone showing Pythagorian numbers (Plimpton 322). 
(Reproduced from Nengefaauer*B Enact Sciences in Antiquity) 

trace it in the heavens. We do not know when 
they came to the knowledge that tW celestial equator 

1300 B.C for some of the ecliptic star-groups like the 
Cancer, or Scorpion are found portrayed on boundary 



stones which can be dated 1300 B.C. Neugebauer 
and Sachs maintain that the ecliptic is first found 
mentioned in a Babylonian text of 419 B.C., but its 
use as a reference plane must have started much 
earlier, probably before 550 B.C. But the steps by 
which the knowledge of stars marking the ecliptic 

Probably the first stage was to determine the 
angular distance of heavenly bodies from some 
'Normal Stars' as indicated by Sachs.* These normal 
stars were stars either on the ecliptic, like Regulus, 
Spica, or a Librae or some other stars close to it. Sachs 
gives a list of 34 such normal stars. Probably the 

Fig. 17— Babylonian Boundary stone showing lunar epheroeris 
engraved on it (A. 3412 Rev.) {Exact Sciences in Antiquity) 

was obtained, are not yet known with precision. 
Only some guesses can be made. 

The early astronomers probably observed that the 
bright stars Regulus ( a Leonis ), Spica ( a VtrginisU 
the conspicuous group Pleiades, and certain fainter 
stars a Librae, a Scorvii were almost on tne suns 
path. The ecliptic could be roughly constructed by 
joining these stars. 

'Regulus* or a Leonis was the 'Royal Star' in 
Babylonian mythology. In Indian classics, it is known 
as Magha (or the Great ) and the presiding deity is 
Jndra, the most powerful Vedic god. It is almost 
exactly on the ecliptic. Citra ( or a Virginis ) is 2° to 
the south. 

The First Point of Aries :— The first point of Aries 
is the fiducial point from which all astronomical 
measurements are made. But how was this point, or 
any other cardinal point, say the first point of Cancer 
( summer solstice ), the first point of Capricornus 
( winter solstice ) and the first point of Libra, were 
located on the circle of the ecliptic in early times ? 

For rarely have the first point of Aries nor any 
other of the cardinal points been occupied by prominent 
stars during historical times. Even if for measurement, 
the ancient astronomers used some kind of astrono- 
mical instrument, say the armillary sphere, it would 
be difficult for them to locate the first point of Aries 
correct within a degree. 

ecliptic positions of these normal stars were 
determined after some effort by some method not yet 
known, and then the positions of other heavenly 

Fig. 18 — Armillary sphere. 
(Reproduced from Kwyclopardia Britamniea). 

bodies referred to the first point of Aries or the 
beginning of a sign could be found. The early 
observations are rough and no accuracy of less than a 
degree is claimed by any classical scholar for them. 

* A. Sachs, Babylonian Horoscopes, p. 53, Journal of Cuneiform 
Studies, VoL VI, No. 2. 



Precession of Equinoxes :— But the first point of 
Aries is not a fixed point on the ecliptic, though all 
ancient astronomers belived it to be fixed once for all. 
It moves steadily to the west at the rate of 50" per 

Ptolemy's first point of Arias T is 4° to the west 
of Hipparchcs's. 

Clay tablet records have been obtained in 
Mesopotamia which have been interpreted as represen- 




=. Vedic Times aboul 2300 B.C. 







Pi.= Ptolemy 

Si = SuryaSicfdhonfa 

M= Modern 

140 B.C. 

150 A.a 
185 AD. 
500 A£. 
570 A.D. 
1S5Q A.D. 

Fig. 19— The Zodiac through ages. 

year. Astronomers of different ages must have given 
measurements of stellar positions from observations 
made either during their own times, or from 
observations made by their predecessors, quite 
unconscious of the fact that the reference point had 
shifted. The result is that the positions of stars given 
by different astronomers of antiquity do not tally, and 
the positions given by the same astronomer are not always 
consistent This is illustrated in Fig. 19 of the Zodiac. 

Let us take Hipparchos's First point of Aries T as 
our standard point. 

ting two systems of Ephemeris known as Systems A and 
B. System B indicates that the vernal point is Aries 8°. 
This indicates that the observations were taken about 
550 years before Ptolemy. This coincides approxi- 
mately with the time of the Chaldean astronomer 
Kidinnu, who observed at Borsippa near Babylon, and 
is taken to be the author of the nineteen-year cycle. 
System A uses Aries 10° as the vernal point ; the 
author of this system might have flourished 120-150 
years before Kidinnu, and may be identified with 
Naburiannu, son of Balatu, who flourished about 490 



B.C. Older still is the use of Aries 15° by Eudoxus of 
Cnidus, the first Greek astronomer to start a geometri- 
cal theory of planetary motion. This refers to 
observations dating from about 810 B.C. These dates, 
before they are accepted, should receive independent 

The Use of Spherical Co-ordinates 

The ancient astronomers were interested primarily 
in the moon and the planets but later about 150 B.C., 
Hipparchos gives lists of fixed stars as well with their 

It was clearly observed that though these planets 
keep near the ecliptic, they deviate by small amounts* 
sometimes to the north, sometimes to the south. In 
the case of the moon, the maximum deviation amounts 
to nearly 5° (inclination of the moon's orbit to the 
ecliptic). In the case of planets, excepting in the case 
of Mercury and Venus, the deviation was not large. 

In the case of the moon, a knowledge of the moons 
celestial latitude was necessary for prediction of 
eclipses and therefore both the celestial longitude and 
latitude used to be recorded by the Chaldean astro- 
nomers of the Seleucidean period. In the case of planets, 
only the celestial longitude appear to have been used. 

The Chaldean astronomers were the first to frame 
lunar and planetary ephemerides (i.e. calculation in 
advance of lunar and planetary positions— the pre- 
cursor of modern Nautical Almanacs and Ephemerides) 
from about 500 B.C. But during these times, neither 
the knowledge of the sphere nor of spherical or 
plane trigonometry had developed. The Chaldeans 
had only developed the ideas of angular measurement 
which they expressed in degrees, minutes and seconds, 
the whole circle being divided into 360° degrees. 
Their methods, which have been elucidated by 
Neugebauer, Sachs and others were arithemetical. 
They took maximum and minimum values of astrono- 
nomical quantities, and interpolated for an inter- 
mediate period, assuming the change to be linear 
(zigzag function, vide Neugebauer, Exact Sciences in 
Antiquity, Chap. V, Babylonian Astronomy). 

It was the Greeks who introduced geometrical 
methods to deal with positions of heavenly bodies, 
and made the next great advance in astronomy- But 
they developed trigonometry only to a rudimentary 
stage ( vide § 4-8). But they also used Babylonian 
arithmetical methods alternately. Thus while Ptolemy 
uses the trigonometric chord functions in his Syntaxis, 
in the astrological text, called Teirabiblos, he uses 
the Babylonian arithmetical methods. 

Though the calendar, as we have seen, gave the 
first stimulus for the cultivation of the astronomical 

science, the use of astronomy for perfecting the 
calender appears in the West to have come to a stop 
after the Seleucidean era. For Rome conquered the 
whole western Asia up to the Euphrates by about 
80 A. D., and the Julian calendar replaced the 
Babylonian luni-solar calendar, which have, however, 
continued to currency probably in limited regions like 
Syria, Arabia and Iraq amongst certain communities. 
The Sassanid Persians also followed their own solar 
calendars inherited from Acheminid times. But the 
elements of the Chaldean luni-solar calendar have 
been used in a limited way, for the Christian 
ecclesiastic calendar for Christianity arose in Palestine 
and Syria, and the most important event in Christ's 
life, His crucifixion, is recorded in terms of the 
luni-solar calendar prevalent in Palestine about the 
first century A.D. 


It has been considered necessary to give a short 
account of Greek contributions to astronomy, because 
there is a widespread vi>w that it was Greek astro- 
nomy which formed the basis of calendar reform in 
India which took place about 400 A.D. ( Siddhanta 
Jyotisa calendar). Let us see how far this view is 
correct. The Greeks themselves appear to have made 
no use of astronomy for the reform of their own 
calendars, as was done later in India. They cultivated 
astronomy partly as pure science, partly as an 
indispensable adjunct to astrology. 

It is now well-known that Greek civilization had a 
long past going back to at least 1500 B.C. The ^remains 
of this civilization have been found in Crete (itfinoan), 
and on the Greek mainland itself (Mycenean). 
Inscriptions have been found in strange scripts (Linear 

A, and B) which defied decipherment till 1952. We 
have therefore as yet no knowledge of the calendar in 
the Mycenean age of Greece (1400 B.C.— 1000 B.C.), 
but probably they will now be forthcoming. 

The Homeric poems 'Iliad' and 'Odyssey' written 
about 900 B.C., as well as Hesiod writing about 700 

B. C. show considerable acquaintance of stars and 
constellations needed for sea-faring people, to find out 
their orientation when out at sea. 

From about 750 B.C., the Greek city-states began 
to emerge ; they were engaged in maritime trade over 
the whole Mediterranean basin. These activities 
brought them into contact with many older nations 
who had attained a high standard of civilization, e.g., 
the Egyptians, the nations of the Near East, vix., the 
Lydians, the Phoenicians, and the Assyrians and 
imbibed many elements of their civilization. The 
older Greek scholars themselves admit that the Greeks 



borrowed their script* from the Phoenicians, their 
coinage from the Lydians, their preliminary ideas of 
geometry from the Egyptians and of astronomy from 
the Chaldeans. But they enriched all these sciences 
beyond measure by their own original thoughts 
and contributions. As Plato (428-348 B.C.) proudly 
remarks : "...whatever the Greeks acquire from foreigners, 
is turned by them into something nobler" 

Greek science goes no further back than Thales 
of Miletus (624-548 B.C. ), who is reckoned to be the 
first of the seven sages of Greece. Considerable 
knowledge of astronomy and physics was ascribed to 
him by later writers. He is supposed to have predicted 
the occurrence of an almost total solar eclipse, which 
occurred on May 28, 585 B.C., on the basis of his 
knowledge of the Chaldean Saros. These stories are 
now disbelieved by scholars well versed in Assynology, 
for according to their finding, the Chaldeans them- 
selves before 400 B.C., had no knowledge of the Saros 
of 18 years 10J days used later to predict the eclipses, 
but they used other methods with only partial success. 
Thales might have used one of these methods, but not 
certainly the Chaldean Saros. Considering the crude 
state of Greek civilization in Thales' times, these 
scholars think that it is a fairytale of modern times 
that Thales knew anything about the Saros. Thales 
lived in a coastal city of Asia Minor which had active 
contact with the great civilizations of the Near East, 
and probably much of the knowledge ascribed to him 
were picked up from Babylon and Egypt. 

The next figure in Greek astronomy is Anaximander, 
( 610-545 B.C. ), likewise of Miletus a junior contem- 
porary of Thales, who is said to have introduced the 
use of the gnomon ( vide § 4"3). This may be conceded, 
but this practice was derived most probably from the 
Chaldeans, who used the gnomon from much earlier 
times. Cleostratos ( 530 B.C. ) of Tenedos was cited 
by later authors to have introduced the knowledge of 
the zodiac, of the eight-year cycle of intercalations in 
Greece, but probably he merely transmitted the 
Babylonian knowledge and practice. Meton of Athens 
is said to have introduced the nineteen-year cycle of 
7 intercalary months in Athens in 432 B.C., but as 
remarked earlier, its use in Greek calendars cannot 
be dated before 342 B.C., though it was known in 
Babylon from at least 383 B.C. The question of 
priority of this discovery is still to be decided, 
probably by fresh finds and interpretation of ancient 

astronomical records. 

"♦Ttl^pearT^t^Greekfl of Homeric poems used linear A 
andB but about 900 B.C., they borrowed the simpler Phoenician 
script' and adopted it to their use by the addition of vowels. 
Thereby they forgot their old script and history, which became myth 
and legend. The decipherment of Minoan Linear B has been 
achieved in 1952 by Ventris and Chadwick. 

We have besides philosophers of the Pythagorian 
school ( 500-300 B. C. ), a religious brotherhood 
which cultivated geometry, astronomy, physics and 
mathematics. They are cited by later writers to 
have propagated the view that the earth was 
a sphere, and the planets were also spherical bodies 
like the earth, but it is difficult to state when, and 
on what grounds these theories were first propounded. 

These were the periods of tutelage. Greek genius in 
astronomy began to flower only after 400 B.C., and 
was aided by a number of causes. 

The first was the development of geometry as a 
science by philosophers of the Pythagorean school 
( 500-300 B. C. ), and other scholars, notably 
Hippocrates of Chios ( 450-430 B.C. ), and Democritos 
of Abdera ( 460-370 B.C.). A great impetus to both 
plane and solid geometry was given by Plato ( 428- 
348 B.C. ), famous philosopher and founder of a 
school of studies and research known to the world as 
the 'Academy*. Plato counted amongst his contem- 
poraries and juniors several geometers of distinction. 
viz.. Archytas of Tarentum (first half of fourth 
century B.C. ), Theaitetus of Athens ( c. 380 B.C. ), 
Eudoxus of Cnidos ( d. 355 B.C. ), and several others. 
All tha geometrical knowledge developed by these and 
other scholars was compiled, and rewritten into a 
logical system with rich contributions of his own by 
Euclid, who lived in the Museum of Alexandria 
( 280 B.C. X And was bequeathed to the world in 
thirteen ( or fifteen ) books known as the Elements 
of Euclid, which have remained to this day the basis of 
the teaching of elementary geometry. There is no 
other book of science which have remained current 
and authoritative for such a long stretch" of time, now 
extending over two thousand years. 

The second factor was political. During the sixth 
and fifth centuries before Christ, the Greek savants 
and scholars had indeed undertaken educational 
journeys to the Near East in search of knowledge 
—journeys which were made possible and safe under 
the orderly regime of the Acheminid empire (Persian). 
But it was the conquest of the Persian empire by 
Alexander of Macedon in 330 B.C., which rendered 
these contacts easier and more fruitful. The Greek 
successor dynasties, viz., the Ptolemaic dynasty in 
Egypt, and the Seleucid dynasty in Babylon and other 
dynasties in Asia Minor were all great patrons of 
learning and encouraged and maintained scholars ; 
the former set up the famous Museum at Alexandria, 
which was a research institution with a great library, 
an observatory and other necessary equipment. It 
attracted scholars from all parts of Greater Greece 
and provided them with free board, lodge and a salary. 
This place nurtured a number of great Greek geniuses : 



Euclid, already mentioned; Eratosthenes who first 
measured correctly the diameter of the earth and 
was the founder of scientific chronology ; and others 
whom we shall meet presently. 

On the Asiatic side, under the centralized rule of 
the Seleucids, the later Chaldean and Greek astrono- 
mical efforts became very much intermingled. A 
Chaldean priest, Berossus, who lived during the reign 
of the second Seleucidean king Antiochos Soter 
( 282-261 B.C. ), translated into Greek the standard 
Chaldean works on astronomy and astrology. The 
period from 340 B.C. to 150 A.D. may be called the 
most flourishing period of astronomical studies in 
antiquity. The Chaldeans figured prominently during 
the earlier part of this period but their methods 
were based on a primitive form of algebra and 
arithmetic. According to Neugebauer, their contri- 
butions in mathematics and astronomy were as good 
as those of the contemporary Greeks who used 
geometry, but they gradually faded into obscurity 
on account of their infatuation with astrology ; and 
the Greeks, though they were great believers in 
astrology, freed themselves at least from astrolatry, 
and cultivated astronomy as part of astrology, and 
emerged as leaders in astronomical science. 

The earliest Greek astronomer to use geometrical 
ideas in astronomy is, if we leave aside the Pytha- 
goreans, probably Eudoxus of Cnidos ( d. 355 B.C. ), 
a junior contemporary, friend and pupil of Plato. 
He made great original discoveries in geometry, and 
Books V and VI of Euclid are ascribed to him. It 
was probably his knowledge of geometry which led 
him to make the first scientific attempt to give a 
geometrical explanation for the irregular motions of 
the sun, the moon, and the planets. Twenty-seven 
spheres, all concentric to the earth were needed to 
account for these motions. This theory had but a 
short life, but it is remarkable as the first instance, 
when heavenly bodies, connected with great gods, 
were treated on a human level. 

Eudoxus is supposed to be the inventor of 
geometrical methods for determining the sizes and 
distances of the sun and the moon, usually ascribed 
to Aristarchus of Samos (ft. 280 B.C.), who is known to 
have taught that the daily revolution of the celestial 
sphere was due to the rotation of the earth round its 
axis. He is also said to have first put forward the 
heliocentric theory of the universe. Neither of these 
theories was accepted by contemporary astronomers. 
The world had to wait for the appearance of a Coper- 
nicus (1473-1543), for the acceptance of these views. 

Apollonius of Perga (born about 262 B.C.) known 
more for his treatise on Conies, originated the theory 

of epicycles, and eccentrics to account for planetary 
motion. He was a junior contemporary of two 
great figures : Eratosthenes already mentioned and 
Archimedes of Syracuse (287-212 B.C.), a great 
figure in mechanics, hydrostatics and other sciences, 
but to astronomy, he is remembered as originator of 
the idea of Planetarium— a revolving open sphere 
with internal mechanisms with which he could imitate 
the motions of the sun, the moon, and the five planets. 

Archimedes is also credited with attempts for 
finding out the actual distances of the planets from the 
earth. We do not know whether this is correct or not, 
but about this time, we find the planets arranged accord- 
ing to the order of their distances from the earth : 

Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn 
or if we take the reverse order : 

Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. 
This last order was taken up by astrology and formed 
the basis of the seven-day week, which came into 
vogue about the first century A.D. 

The greatest name in Greek astronomy is 
Hipparchos of Nicaea, in Bithynia who settled in the 
island of Rhodes and had an observatory there 
(ft. 161-127 B.C.J. He probably corresponded with the 
savants at the Museum of Alexandria. Not much of 
his writings have come down to us, except through 
quotations and remarks by Claudius Ptolemy, the 
famous Alexandrian astronomer who flourished three 
centuries later. Sarton writes about Hipparchos : 

"It is possible that all the Ptolemaic instruments, except 
the mural quadant, had already been invented by him (e.g. 
diopter, parallactic and meridian instruments). He was the 
first Greek observer who divided the circles of his instru- 
ments into 360 degrees. He constructed the first celestial 
globe on record. 

He used and probably invented the stereographic 
projection. He made an immense number of astronomical 
observations with amazing accuracy". 

The principle of measurement of angles was 
certainly derived from the Chaldeans. Hipparchos gave 
a catalogue of 850 stars with their positions which 
is reproduced in Ptolemy's Syntaxis. Vogt found 
that of the 471 preserved numbers giving position, 
64 are declinations, 67 are right ascensions, 340 are 
in polar longitudes and latitudes, which reappear in 
the Surya Siddhanta, six hundred years later. 

It is suggested that after his discovery of precession 
( vide § 4.9 ), Hipparchos probably used celestial longi- 
tudes and latitudes. But these co-ordinates had been 
already used by the Chaldeans at least a century earlier. 

Hipparchos had probably some knowledge of plane 
and spherical trigonometry necessary for the solution 

C. B.-34 



of astronomical problems, e. g., finding out the time 
of rise of zodiacal signs during the year, a problem 
of great importance to horoscopic astrology. It is the 
current opinion that he used the double chord, 
illustrated below : 

Chord (2 a)«2 R Sin a 

Fig. 20 

and gave a table of double-chords from 0° to 90°, 
which was later improved by Ptolemy in his Syntaxis. 
It is suggested by Neugebauer, that the 'Sine function 
(Jy& in Hindu astronomy) was introduced 600 years 
later by Xryabhata, and replaced the double chord. 
The Hindu astronomers used Utkramajya which is the 
ver sine function, 1 — cos a, but do not appear to have 
used the cosine function as such. Neither the Greeks 
nor the Hindus used the tangent, and the cotangent, 
which were introduced by Arab astronomers about the 
ninth century (al-Batt3M, 858-929 A.D.), and were 
known in Latin in early days as Umbra Versa, and 
Umbra Extensa ( extent of shadow ) respectively. 
These are reminiscent of the practice of designating 
the zenith distance Z of the sun by the length I of the 
shadow of the gnomon, l = p tan Z, p being the height 
of the gnomon. 

Between Hipparchos and Claudius Ptolemy 
(150 A.D.), who lived at the Alexandrian Museum 
from 128 A.D. to 151 A.D., there is a gap of 300 
years, which saw the phenomenal rise of horoscopic 
astrology. There are, however, very few great names 
in astronomy. Menelaos, a Greek astronomer who 
lived in Rome about 98 A.D.> laid the foundation of 
spherical trigonometry, but it was confined to a 
transversal proposition from which Ptolemy deduced 
solutions for only right angled spherical triangles, 
of which either two sides or an angle and one 
side are given. The Hindu astronomers likewise used 
only solutions of right angled spherical triangles. 
The discovery of general relations in spherical 
triogonometry was the work of Arabic astronomers 

Claudius Ptolemy who worked at Alexandria 
between 128-151 A.D., was, as Sarton says, a man of 
the Euclidean type. Great equally as an astronomer, 
mathematician, geographer, bhysicist, and chronologist, 
his main work is the great mathematical and astro- 
nomical treatise known in Greek as 'Syntaxis? , and in 

Arabic translation as the Almagest. It has been long 
supposed that it rendered all previous treatises in 
astronomy obsolete, and remained a standard text, 
which fertilized the brains of all ancient and medieval 
astronomers, Greek, Jew, Arab, and European, till 
the rise of the heliocentric theory of the universe 
rendered it obsolete. This opinion appears to have 
been rather exaggerated. Strangely enough, the 
Syntaxis appears to have been quite unknown to Hindu 
astronomers of the 5th century A.D. 

Ptolemy's chief contribution to astronomy was his 
elaborate theory of planetary motion and discovery of 
a second inequality in the motion of the moon, now 
called Evection. He gave a catalogue of 1028 stars 
with their positions, most of which have been shown 
to have been taken from Hipparchos by adding 3° to 
the longitudes given by him. This represents the 
shift of the first point of Aries since Hipparchos's 
time according to Ptolemy's calculation. The actual 
value is 4°. 

Ptolemy wrote a treatise on astrology known as 
the "Tetrabiblos" which long remained the Bible of 
the astrologers. 

After Ptolemy, there were no great figure in 
astronomy except few commentators and workers of 
mediocre ability like Theon of Alexandria (about 
370 A.D.), who initiated the false theory of trepidation 
of the equinoxes, and Paulus of Alexandria (fl. 378 
A.D.) who wrote an astrological introduction. He is 
supposed to have been the inspirer of the Indian 
Siddhanta known as 'PauliM Sid&hania 7 {vide § 5'6 ), 
but this hypothesis started by Alberuni has never 
been proved. With the advent of Christianty, and 
after murder of the learned Hypatia (415 A.D.). the 
light' goes out of Greece. 

The Greek contributions to astronomy are : 

A geocentric theory of the universe, with the 
planets in the order given on page 203. 

The treatment of planets as spherical bodies 
similar to the earth. 

Geometrization of astronomy, development of 
the concepts of the equator, the ecliptic and of 
spherical co-ordinates (right ascension and declination, 
celestial latitude and longitude), some elementary know- 
ledge of plane and spherical trigometry to deal with 
astronomical problems. 

Knowledge of planetary orbits, and attempts to 
explain them with the aid of epicyclic theories. 


In the previous sections, we have stated how the 
Chaldean and Greek astronomers started giving 



positions of planets, and stars, with the point of 
intersection of the ecliptic and the equator — the first 
point of Aries — as the fiducial point. We shall now 
relate how the discovery was made that this point is 
not fixed in the heavens, but has a slow motion 
along the ecliptic, to the west at the rate of ca. 50" 
per year. The rate is very small* but as it is unidirec- 
tional and cumulative, it is of immense importance 
to astronomy, and incidentally is very damaging to 

When the sun, in course of its yearly journey 
arrives at the first point of Aries, we have the vernal 
equinox. The first point of Aries is therefore also 
called the vernal point. 

The position of the vernal point has rarely in the 
course of history, been occupied by a prominent star, 
but in India, as narrated in § 5*4, its nearness to star- 
groups as well as the nearness r of other cardinal 
points to star-groups have been noted from very early 
times. Traditions of different epochs record different 
stars as being near to the cardinal points. But 
nobody app?ard to have drawn any conclusion from 
these records {vide for details § 5'4 ). 

In Babylon also, different sets of positions of 
stars and planets record Aries 15 1 , Aries 10°, and 
Aries 8° (the zero is of Ptolemy's) as being the vernal 
point. But no Chaldean astronomer to our knowledge 
appears to have drawn any conclusion from these data. 

The first astronomer known to have drawn 
attention to the precession of the equinoxes was 
Hipparchos. He particularly mentions that the 
distance of the bright star Spica (a Virginis or Citra) 
has shifted by 2° from the autumnal equinoctial 
point since the time of his predecessor Timocharis 
who observed at Alexandria about 280 B.C. He 
concluded that the autumnal point, and therefore also 
the vernal point, was moving westward at the rate of 
51J seconds per year. 

It is not known whether Hipparchos considered 
the motion as unidirectional. It was impossible for 
him to say anything definite on this point, as 
obeservations extending over centuries are required to 
enable one to make a definite statement on this 

Though Hipparchos made, as time showed, one of 
the greatest astronomical discoveries of all times, 
which is all-invportant for the calendar, as well as for 
astronomy, its great importance does not appear to 
have been realized by either his contemporaries or 
followers for thousands of years. 

Let us, therefore, dwell a little on the consequences 
of this discovery. Later and more accurate observa- 
tions have shown that the rate is nearly 50" per year, 

but is subject to variations which we may disregard at 
this stage. The shift is accumulative and in 100 years 
would amount to 1° 24'; and in about 26000 years the 
first point will go completely round the ecliptic. 
The period depends upon certain factors and is not 

The tropical year, or the year which decides the 
recurrence of seasons, is the time-interval for the 
return of the sun in its orbit, starting from the year's 
vernal equinoctial point to the next vernal equinoctial 
point. If these points were fixed on the ecliptic, the 
tropical year would be the same as the sidereal year, 
which is the same as the time of revolution of the 
earth in its orbit. But since the vernal equinoctial point 
slips to the west, the sun has to travel 360° 0' 0"-50" 
= 359° 59' 10" to arrive at the new vernal equi- 
noctial point, hence the duration of the tropical year is 
less than that of the sidereal year by about 20 minutes. 
In exact terms : 

duration of the sidereal year -365.25636 mean solar days 

tropical „ =365.24220 

at the present time. 

Further Consequences of the Precession 
of the Equinoxes 

We may now consider some consequences of the 
precession of the equinoxes. 

Hipparchos appears first to have marked out the 
beginning of the astronomical first point of Aries. It 
started 8° west of the star a Arietis. Ptolemy had 
found that it had shifted by his time by about 3°, 
and gave the rate of precession as 36" per year. In 
this, he was wrong, the true shift being about 4\ 
Ptolemy in his 'Uranometry' gives the starting point 
of the sign of Aries as 6° to the west of (3 Arietis, and 
the other constellations marked at intervals of 30° 
may be marked out on the zodiac. The picture (Fig. 19) 
gives the boundaries of the different signs according to 
Hipparchos. The boundaries cf the signs of Ptolemy 
would be 4° to the west of those of Hipparchos. 

By the time of Ptolemy, (and probably much 
earlier), a complex system of astrology had developed 
which connected men's destiny in life with the 
position of planets in the different signs at the time 
of his birth (horoscopy). It was claimed that even 
the fortunes of nations and countries could be 
calculated in advance from planetary positions in the 
signs. Though a few rational men like Seneca and 
Cicero were as much sceptical about the claims 
of astrology as the modern man, the general mass 
became converted to its claims, even astronomers not 
excepted. Even the great Ptolemy wrote a treatise 
*The Tetrabiblos 3 exposing the principles of Astrology. 



In fact, belief in astrology was one of the main 
incentives for the observation of the positions of 
heavenly bodies in ancient and medieval times which 
were carried out by medieval astronomers with so 
much zeal under the willing patronage of influential 

The discovery of precession is very disconcerting 
to astrologers, for in the astrological lore, the signs 
are identified with certain fixed star-clusters ; whereas 
precession tends to take them entirely out of these 
star-clusters. Thus since Hipparchoss time, the shift 
has been nearly 30 degrees, and what was the sign of 
Pisces in Hipparchos's time has now become the sign 
of Aries, and the astronomical sign of Aries has now 
nothing to do with the Aries constellation. 

This consequence must have been foreseen by the 
followers of Ptolemy, and they probably started, more 
on psychological than on scientific grounds, to find 
out theories to mitigate the devastating influence of 
precession on astrology. Astronomers immediately 
following Ptolemy barely mentioned precession. It 
was first referred to by Theon of Alexandria (ca. 370 
A.D.) who invented the theory of Trepidation, i.e., he 
said that the precessional motion was not unidirec- 
tional, but oscillatory. He gave the amplitude of 
oscillation as 8°. Probably this figure was suggested 
by the fact that at Theon' s time the first point of 
Aries had shifted by a little less than 8° from 
Hipparchos s position, and Theon thought that it 
would go back and save astrology. 

Proclos the successor (410-485 A.D.), head of the 

Platonic Academy at Athens, a very learned man and 

one of the founders of Neoplatonism, denied the 
existence of precession ! 

After the sixth century A.D„ the dark age set in 
Europe and the mantle of scientific investigation fell 
on the Hindus and the Arabs. Let us see how the 
Arab astronomers regarded the precession. 

Thabit ibn Qurra (826-901 A.D.), who flourished 
at Baghdad under the early Abbasides, translated 

Ptolemy's Almagest into Arabic ; he noted precession, 
but upheld the theory of trepidation. But the other 
great Arabic astronomers like al-Farghanl (861- 
Baghdad), al-Battanl (858-Syria), Abd al-RahamSn 
al-Sufl (903-986-Teheran) and Ibn Yunus (d. 1009— 
Cairo), all noted precession and rejected the theory 
of trepidation. In fact al-Battani gave the rate of 
precession as 54" per year, which is far more correct 
than the rate given by Ptolemy, vh., 36" per year. 

But unfortunately, Europe recovering from the 
slumbers of dark ages were more influenced by the 
Spanish-Muslim astronomers al-Zarquali (L029-1087 of 
Cordova), and al-Bitruji (ca 1150, living at Seville), 
who upheld the theory of trepidation. As their 
influence was considerable, they were largely 
responsible for its diffusion among the Muslim, Jewish 
and Christian astronomers, so much so that Johann 
Werner (1522) and Copernicus himself (1543) were still 
accepting it ; Tycho Brahe and Kepler had doubts 
concerning the continuity and regularity of the 
precession, but they finally rejected the trepidation. 
The theory of trepidation was completely given up in 
Europe after 1687, when Newton gave a physical 
explanation of it from dynamics and the law of 
gravitation. This is given in appendix (4- A), for the 
benefit of Indian astrologers and almanac-makers who 
still believe in the theory of trepidation and oppose 
reform of the wrong calendar they are using for 

Sarton from whose writings much of this account 
has been compiled, writes* : 

"The persistence of the false theory of trepidation is 
difi&cult to understand. At the very beginning of our era, 
the time span of the observations was still too small to 
measure the precession with precision and without 
ambiguity, but as the centuries passed there could not 
remain any ambiguity. Between the stellar observations 
registered in the Almagest and those that could be made by 
Copernicus, almost fifteen centuries had elapsed, and the 
difference of longitudes would amount to 21°" 

* Sarton, A Eisiory of Science, p. 446. 


Newton's Explanation of the Precession 
of the Equinoxes 

In view of the prevailing confusion in the minds of 
Indian almanac makers regarding precession of the equinoxes, 
a short sketch of the physical explanation of the phenomenon 
originally given first by Newton is given here in the 
hope that those amongst Indian calendar makers who 
believe in science, may be persuaded to give up their belief 
in the theory of trepidation and be converted to the 
sayana reckoning advocated in these pages. This 
explanation will be found in any standard book on Dynamics 
or Dynamical Astronomy, e.g., in Webster's Dynamics. 

We have now to regard the earth as a material sphere, 
spinning rapidly round its axes, which is inclined at an 
angle of ? — w to the plane of the ecliptic, where « = obliquity 
of the ecliptic to the equator. 

The earth is kept in its orbit by the gravitational pull of 
the sun, which is situated at one of the foci of the earth's orbit 
which is an ellipse. Dynamics shows that the plane of the 
ecliptic is almost invariant, i.e., does not change with time, 
except a very small oscillation due to attraction of other 
planets on the earth. What is then precession due to ? 

This is explained by means of the following figure. 



Fig. 21 — Showing the precession of the equinoxes. 

In the above figure (No. 21), C is the pole of the ecliptic 
EL'L. Let T ± midway between E and L be the firsj; 
point of Aries for year 1. Then the celestial pole is P 1( 
and the celestial equator is E X T X Q X . Due to precession of 
the equinoxes, the first point of Aries is slowly moving in 
the backward direction 1/ T r E along the ecliptic. If T ± 
ahtfts to T , in year % the celestial pole shifts to P 2 
*long the small circle P* P* P B ...where CP = obliquity of 

the ecliptic. The celestial equator assumes a new position 
E 2 T 2 Q* in year 2. 

The celestial pole P therefore goes round the pole of the 
ecliptic C, and it makes a complete cycle in a period of about 
26000 years as shown in fig. 22. 

At present (1950 A. D.), the celestial pole is 58' from 
Polaris (a Ursce Minoris) which is a star of the second 
magnitude. CP, i.e., the line joining the pole of the ecliptic 
G to the celestial pole P continues to approach the Polaris 
up to 2105 A. D., when the pole would be only 30' away from 
the star and will then begin to recede from it. 

Polaris Q f R ota tion 

Pole Star 

4600 B.a 

d Cygni 

14 800 A.D. 

Fig. 22— Showing the precessional path of the celestial 
4 pole among the stars, 

(Taken from Astronomy by Russell & others) 

It will be seen that the celestial pole has not been 
marked with a prominent star for most part of this period 
of 26000 years. About 2700 B. C, the second magnitude 
star a Draconis was the pole-star, as was probably known 
to the ancient Egyptians, the Chinese and the Rg-Vedic 
Hindus. Conscious human history hardly goes beyond this 
period. The prominent stars which will become pole stars 
in future are : 

7 Cephei 4500 A.D. 

a Cephei... 7500 A.D. 

8 Cygni 11200 A.D. 

a Lyrse (Vega) . . .13600 A.D. 

The last *is a first magnitude star, the brightest in the 
northern heavens and can be easily picked up with the 
naked eye. 




The phenomenon of precession of the equinoxes tells us 
that in addition to rotation, the earth has another motion, 
viz., a slow conical motion of its axis round the pole of 
the ecliptic which causes the equinoxes to move bakward. 
The phenomenon can be visualized by reference to the 
motion of tops played by boys (Fig. 23). 

It is a matter of common experience with those who 
have played with tops that when the top is thrown spinning 
on the earth, the axis round which the top is spinning very 
often is not vertical, but is oblique ; and it is also having a 
slow motion in a circle round the vertical as shown 
in fig, 23. This last motion is precessional motion. The 
top may be likened to the earth, and the vertical direction 
of gravity, corresponds to the pole of the ecliptic. The 

Fig. 23— Motion of a top. 
The spinning top, which is likened to the earth , causes 
precessional motion of its axis. 

top would have fallen but for its spin. When it slows down, 
the top falls down ; the precessional motion of the top is 
due to the pull exerted by the gravity. 

Now turning to the earth, we see that as a first 
approximation, we may take it as a point of mass concentrated 
at the centre, and then deduce its orbit as is done in 
classical planetary theory. This would have been all right, 
if the earth were a homogeneous sphere. But the earth is not 
a sphere, but a spheroid, having its polar axis shorter than 
the equatorial axis by 43 kms. ( — 27 miles). There is an 
equatorial bulge of matter. The pull due to the sun, is now 
equivalent to a force in the ecliptic passing through the centre 
of the "earth defining the orbital motion, plus a couple, which 
tends to turn the equator of the earth into the plane of the 
ecliptic. It is this couple which produces precessional motion. 

For details of calculation the reader may refer to a book 
on Rigid Dynamics, say A.G. Webster, Dynamics, pp. 298-302, 

We mention only the results here : 

If ^ be the angle of precession, i.e., the angle P ± CP a in 
fig. 21. we have due to the sun s attraction 

. 3ym V C — A a ( . sin 2 ^ 

where : 

y = gravitational constant = 6.67 X 10- 8 c. g. s. units ; 

C = moment of inertia of the earth round the polar axis ; 
A = moment of inertia of the earth round an equatorial axis ; 

w = obliquity of the ecliptic ~ 23° 26' 45" ; 
m = mass of the sun = 1.99 X 10 33 gms ; 
r ^distance of the earth from the sun = 1.497 X 10 13 cms ; 

~— tide-raising term ; 
r 3 

1 = longitude of the sun ; 

n — angular velocity of the earth ; 

£ — angular rotational speed of the earth in radians. 

If the earth were a homogeneous sphere, C would be — A r 
and — 0. But taking the polar radius c~a (1- «), where 
€ = ellipticity of the earth, it can be shown that for the earth, 
in which concentric layers are taken to be homogeneous 
(G-A) 1 / , * 


But actually — — — is the mechanical ellipticity of the earth, 


the value of which has been found by observation as — 


Substituting the values as given above in the expression 
d\pft Sym C - A 07 \ 
lU Mr* • "C" «» "(!-«»*) 

we get the progressive part of the solar precession 
-2-46X10- 12 . 

This is in radians per second of time. To convert it to 
seconds of arc per year, we have to multiply the expression 
by 2.063x10 s X3.156X10 7 . 

2.063 X 10 5 being the number of seconds of angle in 
a radian, and 3.156 X 10 7 the number of seconds of 
time in the year. 
We have therefore the rate of solar precession 

= 16."0 per year. 
We have now to calculate the action of the moon which, 
in spite of its much smaller mass, exerts a far larger 
perturbing force as the lunar distance is much smaller. In 

fact the tide raising force (^r~) * or * ne raoon * s m ^Te than 

double that of the sun. This makes the rate of lunar 
precession = 34". 4 per year. 

But there is another complication. The moon's orbit is 
not coincident with he sun's path (ecliptic) but is inclined 
at an average angle of 5° 9', the extreme values being 5° 19' 
and 4° 59'. Further the points of intersection of the moon's 
orbit with the ecliptic travel round the ecliptic in a period of 
18.6 years. The pole of the moon's orbit M therefore moves 
round the pole of the ecliptic C as shown in fig. 24 in a 
period of 18,6 years. The lunar precessional angle \p», has 
therefore to be defined from the instantaneous position of Jf. 

Combination of the two precessional motions* 

The two precessions can be combined as in fig. 24. Here 
C, M are the poles of the ecliptic and of the moon's orbit. 
P is the celestial pole. The solar precession can be 



represented by the vector ^, along the line PS perpendicular 
to CP, but the lunar precession is represented by the vector 
PJR, which goes up and down as M goes round G in a 

_,- : -JF R 

Fig. 24 — Combination of two precessional motions. 

complete cycle of 18.6 years (period of moons node). 
Therefore the motion is equivalent to 

= Cos MPG... parallel to PS. 

$ n =^ m gin MPG... perpendicular to PS. 

This causes certain irregularities in the precessional 
motion and also in the annual variation of the obliquity of 

the ecliptic, which would otherwise have been uniform. 
These periodic (period = 18*6 years) variations are known 
as Nutation. 

Annual Rate of Precessional Motion 

The solar and lunar precessions amount to 50. "37 per 
tropical year, with a very small centurial variation. After 
making necessary corrections for the slight motion of the 
plane of the ecliptic due to attraction of planets, the annual 
rate of general precession in longitude is obtained as 
follows : — 

Rate of precession = 50."2564 +0."0222 T per trop. year, 

where T— Tropical centuries after 1900 A.D. 

The nutation in longitude may amount to ±17. "2 
according to different positions of the lunar node, but its 
effect on the annual rate of precession does not exceed ±5. 8, 
so that the actual precession rate per year may vary 
between 44. "5 to 56. "0. 

The average rate of annual precession is not constant, 
it is very slowly increasing. The annual rate for certain 
epochs along with the period taken by the equinoxes to move 
through 1°, are however stated below : — 

Hate of precession 

2000 B.C. 49."391 


1900 A.D. 50.256 

2000 A.D. 50.279 

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' 43 


Indian Calendar 


The time-periods in Indian history necessary for 
our purpose are shown in the Chronological Table. 

The earliest civilization so far discovered in India 
is the Harappa-Mohenjo-Daro civilization (sometimes 
also called the Indus-Valley civilization) named after 
the two ancient buried cities of Harappa in the 
Punjab and Mohenjo-Daro in Sind. They were first 
brought to light by the late R.D. Baner jee, Superinten- 
dent of the Western Circle of Archaeology of India in 
1924. It has now been ascertained that this 
civilization extended right upto Rupar on the Sutlej 
in the east and to the Narmada valley in the south. 
This civilization was certainly contemporaneous with 
the Mesopotamian civilizations of about 2500 B.C., 
nearly 500 years before the city of Babylon had risen 
to supremacy amongst the cities of Sumer and Akkad ; 
and with the first dynastic civilization of Egypt. How 
far back it projected into the time-scale is not yet 
known, but certainly many thousand years back. 

From the material records of the Indus-valley 
civilization, it is obvious that the Harappa-Mohenjo- 
Daro people had attained to as high a standard of 
civilization, if not higher, as the contemporary people 
of Iraq and Egypt. But the script has not yet been deci- 
phered ; it is therefore difficult to give a chronological 
history, but it is not so difficult to make a study of the 
attainments of this civilization in arts and sciences ; 
they could build well planned cities, used a drainage 
system superior to that of contemporary Egypt or Iraq, 
used copper and bronze, and had evidently evloved a 
highly complex social organization. 

All civilized communities have been found to have 
evolved accurate systems of weights and measures and 
some kind of calendar for the regulation of social 
life. We have some evidences of the use of standard 
weights and measures in the Indus valley. 

But had they evolved a calendar ? The presump- 
tion is that they must have, but nothing has yet been 
discoverd amongst the artefacts left by these people so 
far recovered by the Archaeological Survey which 
throws light on the calendar, or the system of time- 
measurement they used. 

It is held on quite sound grounds that the Harappa- 
Mohenjodaro people were succeeded in the Punjab 
and in the valley of the now lost Sarasvati river by 
the Aryan people who were either autochthonous or 
more probably came through Afghanistan in single or 

successive streams between 2500 B.C. and 1500 B.C. 
Others would go further back in time-scale from 
certain astronomical evidences. 

Few, almost none of the material records or 
artefacts of the early Aryans except some potteries 
tentatively ascribed to them, have so far been 
discovered. Almost the whole of our knowledge about 
them are derived from the hymns of the Rg-Vedas 
which were composed by priestly families amongst 
them in an archaic form of Sanskrit (Vedic Sanskrit), 
in honour of the gods they worshipped ; in these 
hymns are found occasional references to the sun, the 
moon, certain stars, and to months and seasons. Some 
think that there are also references to planets, i.e., the 
Vedic Aryans could distinguish between fixed stars 
and planets, but this is doubtful. From certain 
references which we discuss in § 5.2, we may conclude 
that they used an empirical luni-solar calendar. 
Probably this was used till 1300 B.C. We do not 
come across sufficient material records until we 
come to the time of Asoka about 270 B.C. . 

What was the calendar during the period 
1330 B.C. — 250 B.C. ? The Yajur-Veda, the Brahmanas, 
the Upani$ads and other post Rg-Vedic literature, and 
the early Buddhistic literature contain occasional 
astronomical references, from which the nature of 
the calender used for ceremonical and other purposes 
can be inferred. The interpretation of the texts is 
neither easy, nor unambiguous. The latter part of 
this period has been called by S. B. Dlksit, our pioneer 
in calendar research, as the Vedahga Jyotisa period. 
This is discussed in § 5.4. 

The Vedanga Jyotisa calendar appears to have 
been almost completely free from foreign influence, 
though this point of view has been contested. The 
Persian conqueror Darius conquered Afghanistan, and 
Gandhar, about 518 B.C. ; this region appears to have 
continued under the Achemenids for nearly two 
centuries. The Achemenids used a solar calendar 
probably adopted from Egypt in contrast to the 
luni-solar calendar of India, but this does not appear to 
have disturbed the indigenous luni-solar calendancal 

The Vedahga Jyotisa period, which as we shall 
show, was continued by Indian dynasts up to the time 
of the Satavahanas (200 A.D.), was succeeded by the 
Siddhania Jyotisa period, but the first record of this 
period is available only about 400 A.D. The transi- 




tional period from 100 A.D. to 400 A.D. is one of the 
darkest periods in Indian chronology. Due to 
successive invasions by Macedonian and Bactrian 
Greeks ( Tavanas ), Parthians ( Pallavas X Sakas and 
Kusanas, the period from 300 B.C. to 200 A.D. is one 
of large foreign contacts which profoundly modified 
Indian life in arts, sciences, sculpture and state-craft. 
But the history of this period was entirely forgotten 
and is being recovered bit by bit from inscriptions, 
foreign references, and from artefacts recovered in 
excavations of the sites occupied by invaders of this 
period. Let us give a bird's eye view of the* history of 
this period, imperfect as it is, so that the reader may 
follow without strain our account of the transition of 
the Vedanga Jyoti$a calendar to Siddhantic calendar. 

In 323 B.C., Alexander of Macedon raided the 
Punjab, but this incident by itself had no such 
profound influence on Indian life as is generally made 
out. Its influence was rather indirect. In India, it 
gave rise to a great national movement of unification 
under Candragupta and-Canakya. In the former 
empire of Darius, it gave rise to a number of Greek 
states which became the focus of radiation of Greek 
culture throughout the East. The most important 
were Egypt under the rule of the Ptolemies, with 
capital at Alexandria, and the Near East under the 
Seleucids with capital at Babylon, which was 
succeeded a few years later by Seleucia a few miles 
distant from later Baghdad. In 306 B.C., Candragupta 
and Seleucus faced each other, but the Greek army 
was rolled back to the borders of modern Iran, and 
almost the whole of modern Afghanistan except 
Bactria (modern Balkh) constituting the four satrapies 
of the old Persian empire were ceded to India. They 
continued to be politically and culturally parts of 
India till the tenth century A.D. 

The Mauryas kept out the Greeks till 186 B.C., 
when on the break-up of their empire, the Greek 
settlers in Bactria who had revolted from their 
overlords, the Seleucids, began to make inroads ipto 
India. There -were two rival Greek houses, the 
earlier, the Euthydemids who under Demetrius and 
Menander (175 B.C.) took possession of the Punjab 
and Sind between 180 B.C. to 150 B.C. and threatened 
even Pataliputra but were rolled back beyond the 
Jamuna by the Sungas ; the line of Eukratidas who 
ousted Demetrius and his line from Bactria and 
Afghanistan proper about 160 B.C., reigned in 
Afghanistan up to 50 B.C. But there rose about 
226 B.C., a great barrier between the Eastern Greeks 
(Bactrians and Indian Greeks) and the Western 
Greeks in the shape of the Parthian empire (248 B.C.), 
which became very powerful under Mithradates I 

(175 — 150 B.C.), who controlled the whole of Iran and 
wrested Bactria from the line of Eukratidas in 138 B.C. 

But inspite of these political happenings, Greek 
remained the language of culture throughout the 
whole Near East, from Asia Minor to North- Western 
India. The Parthians since 128 B.C. called themselves 
Thilhellens* or lover of Greek culture and used Greek 
on their coins, and the Graeco-Chaldean method of 
date-recording on their inscriptions. But about 140 
B.C., a new power was on the move, vix., the Sakas 
from Central Asia ; they began to emerge as a ruling 
race from about 138 B.C. In 129 B.C. they attacked 
Bactria, and by 123 B.C. they wrested it completely 
out of the Parthian empire, after defeating and killing 
on the battlefield two successive Parthian emperors, 
vix., Phraates II (128 B.C.) and Artabanus I (123 B.C.). 

The early Sakas appear from their coins to have 
been under the spell of Greek civilization, and 
used Greek as a language of culture and put motifs 
taken from Greek mythology on their coins. Pressed 
by the next Parthian emperor, Mithradates II 
(123—90 B.C.), they poured by 80 B.C., into the 
whole of what is modern Afghanistan, except the 
Kabul valley, which the Greeks held for sometime. 
Their new territory became known as 'Sakasthan* 
comprising modern Afghanistan and parts of N.W. 
India. From Afghanistan, they poured in successive 
streams to Malwa, Guzrat, Taxila about 70 B.C., and 
to Mathura, somewhat later and had put an end to 
the numerous Greek principalities in the Punjab. 
Their further progress was barred by the Satavahanas 
in the South, and numerous small kingdoms which 
arose in the Gangetic valley on the break-up of the 
Sunga and Kanva empires (45 A.D.). After 50 A.D., 
the Sakas of the North were supplanted by the Kusanas 
belonging to a kindred race, and speaking the Saka 
language ; they ruled Northern India from their 
capitals at Peshawar and Mathura up to at least 170 
A.D. Contemporaneously with them, were the Saka 
Satrap houses of Ujjain, who started ruling from 
about first century of the Christian era. 

A chart of these historical incidents is attached 
for the sake of elucidation as they are necessary 
for the comprehension of the extent and amount of 
Greek culture, which was propagated into India, not 
so much through the Greeks directly, but as it appears 
now, indirectly through the early Sakas and their 
successors, the Kusanas. 

It now appears very probable that it was during 
the regime of the Saka and Kusana ruler s (100 B.C.- 
200 A.D.) that a knowledge of the Graeco-Chaldean 
astronomy, which had developed in the Grecian world 
after 300 B.C., and ended with the astronomer 



Ptolemy (150 A.D.), and in the Near East under the 
Seleucids (300 B.C. to 100 A.D.), penetrated into 
India, being brought by astronomers belonging to the 
Saka countries, who later were absorbed into Indian 
society as &akadvipi or Scythian Brahmins. The 
borrowings appear to be more from Seleucid Babylon 
than from the west. The knowledge of Graeco- 
Chaldean astronomy was the basis on which the 
calendar prescribed by the Surija Siddhanta and other 
Siddhantas were built up. It completely replaced the 
former Vedanga Jyotisa calendar and by about 400 A.D, 
when the Vedanga Jyotisa calendar had completely 
disappeared from all parts of India. 

From 400 A.D. to 1200 A.D., almost the whole of 
India used calendars based on Siddhanta Jyotisa for 
date-recording. All Indian astronomers used the 
Saka era for purposes of accurate calculations, but its 
use for date-recording by kings and writers was 
generally confined to parts of the South. In general, 
the Indian dynasties used eras of their own, or regnal 
years, though the annual calendar was compiled 
according to rules laid down either in the Surya 
Siddhanta, the Arya Siddhanta or the Brahma 
Siddhanta, These did not much differ in essentials. 

When India since 1200 A.D. fell under Islamic 
domination, the rulers introduced the lunar Hejira 
calendar for civil and administrative purposes as well. 
Indian calendars were retained only in isolated 
localities where Hindus happened to maintain their 
ndependence, or used only for religious purposes. 
The emperor Akber in 1584 tried to suppress the 
Hejira calendar for administrative purposes by the 
Tarikh-llahi, a modified version of the solar calendar 
of Iran, but this fell in disuse from about 1630. Since 
the advent of British rule in 1757, the Gregorian 
calendar has been used for civil and administrative 
purposes, which is still being continued. 

We have attempted to give below short accounts 
of calendars in use in different epochs of history. 

( —1200 B.C. ) 

The Vedic Literature : The knowledge of the calen- 
dar in this age can be obtained only from the Vedic 
literature which consists however of different strata, 
greatly differing in age. According to the great 
orientalist Max MUller four periods each presupposing 
the preceding can be distinguished. They are 

(a) The Chandas and Mantras composing the 
Safnhiias or collections of hymns, prayers, incantations, 
benedictions, sacrificial formulas, and litanies 

comprising the four Vedas : The Rk t Sama, Yajus 
and Atharva. 

(b) The Brdhmanas which are prose texts contai- 
ning theological matter, particularly observations on 
sacrifices and their mystical significances ; attached 
to the Brahmanas, but reckoned also as independent 
works are the Aranyakas or Upanisads containing 
meditations of forest hermits and ascetics on* God. the 
world, arid mankind. These treatises are attached to 
each of the individual Vedas. 

(c) The Sutras or Aphorisms, or Veddngas. 
'Vedaiigas\ lit. limbs of Vedas, are post-Vedic 

Sutra or aphorism literature which grew as results of 

attempts to understand the Vedas in their various 

aspects, and sometimes to develop the ideas contained 

in the Vedas. According to the orthodox view, there 

are six Veddngas as follows : 

(1) Siksd : or phonetics ; texts explaining how 
the Vedic literature proper is to be pronounced, and 

(2) Kalpa : or ritualistic literature, of which 
four types are known : Srauta Sutras dealing with 
sacrifices ; Qrhya Sutras dealing with domestic duties 
of a householder ; Dharrna Sutras dealing with 
religious and social laws ; Sftlva Sutras dealing with 
the construction of sacrificial altars. 

(3) Vyakarana : or Grammar, e. g. 9 Panini's famous 
Astddhyayii which once fpr all fixed up the Sanskrit 
language. The As\adhyayi is however the culmination 
of attempts by large number of older authors, whose 
works were rendered obsolete by Pacini' masterpiece. 

(4) Nirukla or Etymology: explanation of the Vedic 
words ascribed to one Yaska, who lived before Panini. 

(5) Chandas— Metrics ascribed to Pingala. 

(6) Jyotisa— Astronomy: the Rg- Jyotisa is ascribed 
to one Lagadha, of whom nothing is known. 

Only the sixth Vedanga or Jyotisa interests* us, 
though there are occasional references to the calendar 
in all Satra literatures. 

Age of the Vedic Literature * 

The above gives the 'Philologists' stratification of 
the age of the Vedic literature. About the actual 
age of each strata, there is great divergence of opinion, 
though it is admitted that the oldest in point of age 
are the Safnhitcis. then come the Brahrnanas and 

* Much of the substance-matter of this section is taken from 
Winternitz's A History of Indian Literature Vol. I, published by the 
University of Calcutta. Chap. I, on Vedic literature. 



Upanisads, next the Sutras or the Ved&figas. Of 
the four Vedas, the Rg- Vedas are by common consent 
taken to be the earliest in age and as Winternitz 
remarks, though all subsequent Indian literature refers 
to the Rg-Vedas, they presuppose nothing extant. 

Max Mtiller made a rough assignment of age to 
the different strata as follows on the assumption that 
the BrSThmanic and Upanisadic literature predated 
the rise of Buddhism, and that the Sutra literature 
which may be synchronous with the Buddhistic 
literature may be dated 600 B.C. to 200 B.C. Working 
backwards he assigned the Brahmanic literature to 
600 B.C. to 800 B.C., the interval 800 B.C. to 1000 B.C. 
as the period in which the collections of hymns were 
arranged, and 1000 B,C. to 1200 B.C, as the period of 
the beginning of Vedic poetry. He always regarded 
these periods as terminus ad quern, and in his Gifford 
Lectures on Physical Religion in 1889, he expressly 
states "that we connot hope to fix' a terminus a quo. 
Whether the Vedic hymns were composed 1000, 1200, 
2000 or 3000 years B.C., no power on earth will ever 
determine. * 

It is not correct therefore to say, as some people 
say, that Max Mtiller had proved that 1200-1000 B.C. 
is the date of the Rg- Vedas. t 

Other authorities, Schrader, Tilak, Jacobi, and 
P. C. Sengupta have found much older age for Rg- Vedic 
Indians : in fact, even as early as 4000 B.C., for some 
incidents described in the Rg-Vedas.* But their 
arguments, being based on interpretations of vague 
passages assumed to refer to astronomical phenomena 
have not commanded general recognition. 

Let us first look at the strata within the Rg-Veda 
itself. The Rg-Vedas are divided into 10 Mandalas 
( lit circles ) or books. Of these, the 2nd to the 8th 
books are ascribed to certain priestly families, eg, 
the 2nd book is ascribed to Gritsamadas, the 3rd to 
the Vi§v&mitras, etc. These are agreed to be the 
oldest parts of the Vedas. 

The ninth book is devoted to Soma which is an 
intoxicating drink pressed out of a plant. The drink 
was dear to the Aryans and is also mystically 
identified with the Moon. 

* For details about Vedic antiquity, see Ancient Indian 
Chronology by P. C. Sengupta. 

+ It appears that Max Midler lias been a bit. dogmatic in his 
opinion. Shortly after his death the names of the Vedie gods, Indi a, 
Varufta, Mitra and the Nasatyas in their Kg- Vedic forms were 
discovered in the Hittitc clay tablets discovered at Hoghnz Knei in 
Aeia Minor. They have been assigned to about 145U B.C. More 
evidences about the Vedic Aryans were discovered in the excavations in 
the SarasvatI valley now being undertaken by the Arehaelogical Dept. 
of the Govt, of India. Further, fresh evidences are expected also in 
the archaelogical work undertaken in Afghanistan, Iran and Central 

The first and the tenth books are miscellaneous 
collections ascribed to different authors. They are 
taken to be the latest in age. 

The Rg-Vedas consist of 1028 hymns, containing 
over 40,000 lines of verses. 

The Vedas are regarded as '&rutis' or 4 revealed 
knowledge preserved by hearing." According to 
savants, they were the outpourings of the heart and 
mind, of ancient priestly leaders, to their gods which 
were mostly forces of nature, intermingled very often 
with secular matter. Priestly families were trained 
to memorize the texts and pass them on to succeding 
generations in ways which guaranteed their transmi- 
ssion without error or alteration of the text. 
Savants are almost unanimous in their opinion that 
the Rg-Vedic texts which were composed in an archaic 
form of Sanskrit, which was not completly understood 
even in 500 B.C„ have come to us without change. 
The orthodox Indian view that they are revealed 
knowledge is of course not shared by scholars, both 
eastern and western, who point out that very often 
in the text of the Vedas themselves and in Anukramatyis 
or introductions to texts, the authors of each hymn 
are mentioned by name and family. 

To which locality are the Vedas to be ascribed ? 

As regards locality, they are certainly to be 
ascribed to parts of Afghanistan, east of the Hindukush 
and the Punjab. The rivers of the Punjab, the 
Indus and its tributaries on both sides and the now 
lost SarasvatI are frequently mentioned, the Ganges 
only once in a later text. The authors call themselves 
Aryas or Aryans, in contrast to the Dasas or Dasyus 
who were alien to them, and with whom they came 
in frequent clash. The Dasyus are now taken to be 
partly Indus valley people, partly aboriginals. 

The Rg-Vedas describe a highly complex society 
of priests, warriors, merchants and artisans, and slaves 
but the rigid caste system had not yet developed. 
There are also references to cities, but no artefacts 
except some pottery, have yet been discovered which 
can be referred to the Rg-Vedic Aryans. 

The Rg-Vedic Aryans, it appears, were con- 
temporaneous (if not older) with the great civilizations 
of Mesopotamia, both Sumerian, and later Accadian, 
and according to one view, some of the royal families 
of Asia Minor, were probably 'Vedic, Aryans'. It is 
therefore quite probable that they had attained as 
high a stage of civilization as that of Egypt of the 
Pyramid builders (2700 BC), or of Sumer and Accad 
under Sargon I. 

Let us see what information we can gather about 
the calendar which they must have used, for no 
civilized community can be without a calendar. 


Further, the whole life of Vedic Aryans was centred 
round sacrifices to their great gods ; and sacrifices had 
to be carefully timed with respect to seasons and 
moon's phases. In fact, some sacrifices were year-long, 
as Dr. Martin Haug. the great Vedic scholar remarks 
in his introduction (p. 46) to Ailareya Brahmana 
(affiliated to the Rg-Veda). 

"The Sattras [or sacrifices] which lasted for one year, 
were nothing but an imitation of the sun's yearly course. 
They were divided into two distinct parts, • each of six 
months of thirty days each ; in the midst of both was the 
Vwvan, i.e., equator, or central day, cutting the whole 
Sattra into two halves*. 

This refers to somewhat later times than the 
Rg-Veda, but even during these early times, the 
sacrificial cult was fully developed. Let us see what 
references we get about the calendar from the 
Rg-Vedic times. 

Calendarie and Astronomical References 
in the Rig-Vedas 

These are few, and interspersed along with other 
matter This is not to be wondered at, for the hymns 
are addressed chiefly to the gods, Agni (sacrificial 
fire) Indra (the national warrior god), etc., and other 
references are only incidental. The direct references 
are found only in Books 1 and 10 which are later in 
age than the family books. 

Let us give the texts of a few hymns and their 

translations in English. 

Rg-Veda. 1.164.11 

Dvadasararh nahi tajjaraya varvarti cakram 


A putra agne mithunaso atra sapta satani 

vimsatisca tasthuh. 

Translation : The wheel (or time) having twelve 
spokes revolve round the heavens, but it does not 
wear out. Oh Agni! 720 pairs of sons nde this 

Here the year is likened to a wheel, having 12 
spokes (or months) ; the 720 pairs of sons are 360'-days 
and nights. 

The interpretation commonly accepted is that the 
year was taken to consist of 360 days divided into 12 
months, and the night and the day (following or 
preceding) constituted a couple. 

Ifg-Veda. 1.164.48. 

Dvadasa pradhayaseakramekam trini nabhyani 

ka u tacciketa 

Tasmin tsakam trisata na sankavo'rpitah 

sa?tirna calacalasah. 


Translation : Twelve spoke-boards : One wheel : 
three navels. Who understands these ? In these there 
are 360 sankus (rods) put in like pegs which do not 
get loosened". 

The year is compared to a revolving wheel, whose 
circumference is divided into 12 parts (twelve months). 
They are grouped into three navels (seasons). 

Here also we have a year of 360 days, divided into- 
12 months, four months constituting a season, as we 
find in the oldest inscriptions. 

If the interpretation of the last passage is correct, 
we have the earliest reference to the later caturmasy* 
system, or division of the year into three seasons each 
of four months. 

It appears from these passages that Vedic Aryans, 
had once a year of 360 days as ancient Egyptians also- 
had but they discovered later that this was not the 
correct value either for 12 lunar months, or for a 
seasonal year. For the following reference shows that 
they used also a thirteenth month. 

Jig-Veda, 1.25.8 

Veda maso dhvtavrato dvadasa prajavatah 

vedaya upajayate. 

Translation: Dhftavrata ( Vamna) knows the 
twelve months : (and) the animals created during that 
period ; (and) he knows (the intercalary month> 
which is created (near the twelve months). 

This passage makes it clear that the calendar 
was luni-solar. But how was the adjustment made ? 

A hymn in the Gg-Veda first noted by Tilak 
comes to our help. 

Ilg-Veda, 4.33.7 

Dvadasa dyun yadagohyasya tithye ranannrbhabat 


Suksetrakrnvannanayam ta sindhun dhanvatistha 

nnosadhir nimnamapalj. 

Translation: When the #bh™ sleeping for 
twelve days have made themselves comfortable as 
guests of the unconcealable (sun), they bring the fields 
in good order and direct the rivers. The plants ^grow 
in wildernesses, and lowland is spread with water \ 

According to Tilak, the Ifbhus are the genii of 
seasons. They are said to enjoy the hospitality of 
the sun for twelve days in the above verse. This 
passage, according to Tilak means the adjustment of 
the solar year with the lunar (i.e., 366—354 = 12 

* r/. Ancient Indian Chronology, Chapter VI. 



Another hymn from Atharva Veda (4.11.11) states 
that : 'PrajSpati, the lord of yearly sacrifices after 
finishing one year's sacrifice, prepared himself for the 
next year's sacrifice*. 

The sacrificial literature of India still preserves 
the memory of these days by ordaining that a person 
wishing to perform a yearly sacrifice should devote 
12 days (dvadasaha) before its commencement to the 
preparatory rites. 

Did the Rg-Vedic Aryans have any knowledge 
of the lunar zodiac, or designate the days by the lunar 
mansions, as we find widely prevalent during later 
times ? 

There is no explicit reference to this point, but 
words which are now used to denote the lunar 
mansions are found in several verses of the Rg- 
Vedas, e.g., 

Citra" ( rt Virginia) is mentioned in RV. 4-51-2 
Magna" (a Leonis ) is mentioned in RV. 10-85-13 

but in these passages the meaning of these words is 

not very clear. 

The following references are more explicit. 

J?g- Veda, 5. 54. 13 
Yusma dattrasya Maruto vicetaso ray all syama 
rathyo vayasvatah na yo yucchati tisyo yatha 
divo'sme raranta Marutah sahasrinam. 
Translation : You wise Maruts, we would like to 
be disposer of the wealth conferred by you on us it 
should not deviate (from us) as Tisya does not deviate 
from the heavens. 

Here one is tempted to identify the word 'Tisya' with 
the lunar asterism of that name, vi% t , Pusya (S Cancri). 
The following reference is more explicit. 

Rg- Veda, 10. 85. 13 

Suryaya vahatuh pragat savita yamavasrjat 
Aghaau hanyante gavo'rjunyori paryuhyate. 

Translation ; The (dowry) of cows which was 
given by Savita (Sun) had already gone ahead of Surya. 
On the Agha-day, the cattle were slain (acc. to Sayana 
had departed), on the two Arjuni- days, she was led 
to the bridegroom's house. 

This passage occurs in the famous bridal hymn, 
where the Sun god (Savitr) gives away his daughter 
Surya to Soma (Moon) in marriage. It says that on the 
Agha~day the cows, given as bridal dowry are, driven 
away ; on the two Arjunl-d&y% the bride goes to the 
bridegroom's house. 

This hymn is repeated in the Atharva Safnhitd 
as follows : 

Atharva Safnhita, 14.1.13 
Suryaya vahatmi pragat savita yam avasrjat 
Maghasu hanyante gavah phalgumsu vyuhyate. 

Translation : The first line is identical. In the 
second line, the only change is Magha for Agha, and 
Phalgunl for Arjunz. In the lunar zodiac, Magha 
stands for lunar asterism No. 10, of which the chief star 
is a Leonis. The two Phalgunl stars, Uttara Phalgunl 
(No.12) and Purva Phalgunl (No. 11) stand for Leonis 
and 8 Leonis. 

This verse shows that the custom of designating 
the day (it means day and night) by the lunar asterism 
in which the moon is found in the night, which is 
found widely in vogue in later times, and is used even 
to-day for religious purposes, was in use at the time 
when this hymn was written. The practice therefore 
dates earlier than 1200 B.C. at least. 

Longer periods of Time : The Yuga 

'Yuga is a very common word used in Indian 
literature of all times to denote an integral number of 
years when certain astronomical events recur. It 
exactly corresponds to the Chaldean word 'Saros' 
which has gone into international vocabulary. In 
later Indian literature we have Yugas of all kinds : the 
five yearly yuga, sixty yearly yuga, and Mahayugas of 
4*32 xlO 6 years. Was any Yuga, known in Rg-Vedic 
times ? 

There is evidence that some kind of a short period 
yuga, probably the five yearly yuga of later times, in 
which the moon's phases roughly recur, and which 
was the chief theme of the Vedanga Jyotisa was 
known in Rg-Vedic times as the following quotation 
shows : 

Rg-Safnhita, 1.158.6 
Dirghatama mamateyo jujurvan dasame yuge 
apamartham yatinam Brahma bhavati sarathhS. 
Translation : Dirghatama the son of Mamata 
having grown old in the tenth yuga became the 
charioter of the karma which leads to semi-result. 

The most rational explanation of the word yuga 
here is probably the five yearly yuga of Vedanga 
Jyotisa for it is rational to expect that a man becomes 
old after he attains the 50th year. But there have 
been other explanations. 

The Seasons and the Year 

The most commonly used word for year in the 
Indian literature is Varsa or Vatsara. The word 
4 Versa is very similar to Varsa, the rainy season, and 
is probably derived from it. But curiously enough, 
this word is not found in Rg-Vedas. But the words 
&arad (Autumn), Hemanta (early Winter) etc., ate very 
often found to denote Reasons' and sometimes years, 



just as in English we very often say l A young lady of 
eighteen summers'. 

Summary : The above passages show that the 
Rg-Vedic Aryans, who must be placed at least before 
1200 B.C., had a luni-solar calendar, and used 
intercalary months. We do not have, however, their 
names for the 12 months, and there is no clue to find 
out how the intercalary month which is mentioned 
at one place was introduced. It appears ihat they 
denoted individual days by the naksaira i.e., by the 
lunar asterism in which the moon is found at the 
night, and hence it is permissible to deduce that they 
used the lunar zodiac for describing the motion of 
the moon. There is no mention of the tithi ^or the 
lunar day) widely used in Indian calendars, in the 
Rg-Vedas. The solar year was probably taken to 
consist of 366 days, of which 12 were dropped for 
luni-solar adjustment. 


The Atharva Veda consisting mostly of magic 
incantations also contain calendaric references, but 
we shall make only occasional use of them, as the text 
of this Veda has not probably come to us in unadul- 
terated form, for the Atharva Veda was not regarded 
as holy as the Rg-Veda. 

Of the two other Vedas, the Sama-Vedas contain no 
new matter than what is contained in the Rg-Veda. 
But there are copious calendaric reference in the 
Yajurveda for obvious reasons, which are clearly 
brought out in the following extracts from Winternitz's 
introductry remarks to Yajurvedic studies (p. 158-159) : 

"The two Sarhhitas [Rk and Atharva] which have so far 
been discussed have in common the fact that they were not 
compiled for special liturgical purposes. Although most 
of the hymns of the rJg-Veda could be, and actually were 
used for sacrificial purposes, and although the songs and 
spells of the Atharvaveda were almost throughout employed 
for ritualistic and magic purposes, yet the collection and 
agrrangement of the hymns in these Samhitas have nothing 
to do with the various liturgical and ritualistic purposes. 
The hymns were collected for their own sake and arranged 
and placed, in both these collections, with regard to their 
supposed authors or the singer- schools to which they 
belonged, partly also according to their contents and still 
more their external form-number of verses and such like. 
They are as we may say, collections of songs which pursue a 
literary object. 

It is quite different with the Samhitas of the two other 
Vedaa, the Samaveda and the Yajurveda. In these collections 
we find the songa, verses, and benedictions arranged 

according to their practical purposes, in exactly the order in 
which they were used at the sacrifice. These are, in fact, 
nothing more than prayer-books and song-books for the 
practical use of certain sacrificial priests — not indeed 
written books, but texts, which existed only in the heads of 
teachers and priests and were preserved by means of oral 
teaching and learning in the priests' schools.* 

The Yajurvedas were compiled for the use of the 
Adhvaryu priest " Executor of the Sacrifice" who performs all 
the sacrificial acts, and at the same time uttering prose 
prayers and sacrificial formulae (Yajus). They are the 
liturgical Samhitas, and prayer books of the priests. 

Winternitz gives reasons to believe that the 
Sarhhitas of the Black Yajurveda school are older than 
those of the White school. 

Even such a conservative thinker as Berriedale 
Keith gives 600 B.C. as the terminus ad quern for the 
verses of the Yajurveda Samhita". As we shall see, 
there are references which point to a much earlier 

The Yajur-Veda gives the names of twelve months, 
and the names of the lunar mansions with their 
presiding deities, and talks of the sun's northernly and 
southernly motion. We do not give the texts here, 
but only Dr. Berriedale Keith's translation. 

Taittiriya Safnhita, 4.4.11 

(a) (Ye are) Madhu and Madhava, the months 

of Spring. 

(b) (Ye are) Sukra and Suci, the months of Summer. 

(c) (Ye are) Nabha and Nabhasya, the months 

of Rain. 

(d) (Ye are) Isa and Drja, the months of Autumn. 

(e) (Ye are) Sahas and Sahasya, the months 

of (Early) Winter (Hemanla). 

(f) (Ye are) Tapas and Tapasya, the months of 

cool season. 

* There are two schools of the Yajurveda Samhita each with 
a number of recensions as shown below : 

1. The Black Yajurveda School, with the following recensions : 

fa) TheKathaka 

(b) The Kapisthala-Katha-Samhita, which is preserved only 
in a few fragments of manuscript. 

(c) The Maitrayani-Samhita— shortly called M. 6. 

(d) The Taittiriya-Samhita, also called "Apastamba- 
Samhita" after the Apastamba-School, one of the chief 
schools in which this text was taught— shortly called T. S. 

These four recensions are closely inter-related, and are designated 
as belonging to the "Black Yajurveda*'. Differing from them is the 
White Yajurveda which is known as 6ukla Yajurveda. 

2. The Vajasaneyi-Samhita shortly called V. S. which takes its 
name from Yajfiavalkya Vajasaneya, the chief teacher of this Veda. 
Of this Vajasaneyi-Samhita there are two recensions, that of the 
Kanva and that of the Mfidhyandina-Bchool, which however differ- 
very little from each other. 



The month-names which are- given here and 
repeated in many other verses of the Yajur-Veda 
have been interpreted by all authorities to be tropical. 
Further this is probably the earliest mention of month- 
names in Indian literature ; these names are no longer 
in use, and have been replaced by lunar month-names 
{Caitra, Vai&akha, etc,) which are, however, found at a 
later stage. 

Madhu and Madhava have been taken in later 
literature to correspond to the time-period when the 
sun moves from -30° to 30° along the ecliptic, and 
so on for the other months. But we have no reason 
to believe that the Yajurvedic priests had developed 
such a fine mathematical sense of seasonal definition. 
But it is almost certain that they must have developed 
some method of observing the cardinal points of the 
sun's yearly -course, viz., the two solstices and the 
equinoxes. From these observations, they must have 
counted that the number of days in a year was 366 in 
round numbers. 

The Yajur-Veda speaks in many places of the 
UttarViyana, the northernly course of the sun from 
winter solstice to summer solstice and the Daksinayana 
or the southernly course from summer solstice to 
winter solstice and the Visuvan, or the equinoctial 
point. The ayanas or courses must have received 
their designation from daily notings of sunrise on the 
eastern horizon. The year-long observation of shadows 
cast by a gnomon, of which we have evidences, may 
have formed an alternative method for fixing up the 
solstitial days, and the cardinal points on the horizon, 
(vide Appendix 5-C), where some passages from the 
Aitareya Brahmaiia attached to the Rg-Veda are 
stated in favour of the view that the cardinal points 
were observed by means of the gnomon. 

Once they learnt to anticipate the cardinal days, 
determination of the month-beginnings marking seasons 
would not be difficult. The Madhu-month (the first 
month of spring) would begin 30 or 31 days before the 
vernal equinox day or 61 days after the winter solstice 
day, and the Madhava month on the day after the 
equinoctial day and so on. Average length of 30£ 
days would be given to each month, or 30 and 

31 days to the two months forming a season. 

The Nakshatras 

One of the peculiar features of the Indian 
calendars is the use of the Naksatras as explained in 
§ 41. Evidences have been given that the custom 
started from Rg-Vedic times. But we come across a 
full list of Naksatras only in the Yajurveda with 
names of presiding deities as given in Table No. 10 
( p. 220 ), taken from Dlksit's Bharatiya Jyotifastra. 

There are several points to be noticed in this list,, 
which compared with the list given on p. 210. 

First, the naksatras start with Kfttikas which all 
authorities identify with the conspicuous group 
Pleiades. What is the significance of this ? 

At the present times, the naksatras start with 
AMni, of which the junction star is a or Arietis. 
This custom, Asvinyadi, was introduced in Siddhanta 
Jyotisa time ( 500 A.D. ), when the astronomical first 
point of Aries was near the end of the Revatt 
naksatra ( ( Pisdum ), or the beginning of ASvini. 
We do not enter into the controversy about the exact 
location of this point by the Siddhanta astronomers, 
which is fully discussed in Appendix 5-B. At present, 
the astronomical first point had shifted by as much as 
19° from £ Piscium, but the orthodox Indian calendar 
makers do not admit in the continued precession of the 
equinoxes, and still count the naksatras from Asvini. 

In all older literatures, on the other hand, including 
the great epic Mahabhdrata, whose composition or 
compilation may be dated about 400 B.C., the first 
naksatra is Kfttikd. It therefore stands to reason to 
assume that at one time, when the naksatra enumeration 
started, the Pleiades were close to the astronomical 
first point of Aries, or rose near the true east. This 
is implied in the following verse which S. B. Dlksit 
picked out of the j&atapatha Brahmana : 

&atapatha Brahmana, 2.1.2. 

Ekarh dve trini catvariti va anyani 
naksatranyathaita eva bhfiyistha yat krtfcika.... 
Eta ha vai pracyai diso na cyavante 
sarvani ha va anyani nalisatrani 
pracyai disascyavante. 

Translation : — Other naksatras have one, two, 
three or four ( stars ) only ; these Kfttikas have many 
( stars ).. .They do not deviate from the east; all 
other naksatras deviate from the east* 

The names as given in this list are somewhat 
different from those now adopted, which have come 
into vogue since 500 A.D.; for example, we have : 

No. 6 Tisya for Pusya 

No. 16 Rohini for Jyestha 

( There are thus two Rohinls, No. 2, and No. 16 

No. 17 Vicrtau for Mala 

No. 20 Srona for Sravana 

No. 21 Sravistha for Dhanistha 

No. 23 Prosthapada for Bhadrapada 

No. 26 Asvajuya for Asvini 

No. 27 ApabharanI for Bharanl 

The more important question is whether the lunar 
mansions denote definite clusters of stars, or the 
naksatra-di visions of later times, amounting t6 13° 20' 
or 800' minutes ? This point has been discussed in 3 4*1. 

C. E.-36 


Table 10. 

Names of Nakshatras in the Yajurveda with their Presiding Deities 













Name of 


( Grammatical) 



Purva Phalguni 
Phalgun f 

Uttara Phalguni 



Mulabarhani, Mula 



24. Prosthapada 








7] Tauri 


a Tauri 



\ Orionis 





a Orionis 





j8 Geminorum 



8 Cancri 



€ Hydrae 


i ILL 


a Leonis 



S Leonis 



(3 Leonis 



8 Oorvi 

Tndvn. Tvasta 


a Virginis 



a Bootis 



a Librae 



S Scorpii 



a Scorpii 



X Scorpii 

, Nirrti, Prajapati 


A pah 


S Sagittarii 



a Sagittarii 



a Lyrae 



a Aquilae 



£ Delphini 

Indra, Varuna 


X Aquarii 



a Pegasi 




7 Pegasi 




f Piscium 



/? Arietis 



41 Arietis 


59° 17' 39" 
69 5 25- 
83 31 

88 3 22 


112 31 

128 1 

131 38 59 

149 8 1 

160 36 52 

170 55 23 

192 45 23 

203 8 37 

203 32 8 

224 23 7 

241 52 23 

249 3 51 

263 53 14 

273 52 55 

281 41 11 

284 36 54 

301 4 16 

315 38 38 

340 52 38 

352 47 19 

8 27 32 

19 10 40 

33 16 18 

47 30 19 


+ 4° 2' 46" 

- 5 28 14 

- 13 22 32 

- 16 1 59 

+ 6 40 51 

+ 4 32 

- 11 

6 25 
27 48 

+ 14 19 58 

+ 12 16 13 

- 12 11 31 

- 2 3 4 
+ 30 46 3 

+ 20' 19 

- 1 58 49 

- 4 33 50 

- 13 46 56 

- 6 27 58 

- 3 26 36 

+ 61 44 7 

+ 29 18 18 

+ 31 55 21 

- 23 8 
+ 19 24 25 

+ 12 35 55 

- 12 52 
+ 8 29 7 
+ 10 ~ 26 48 

* S= Singular ; D = 

The Lunar Month-Names 

The solar month -names given earlier have not 
gone into general currency. The month-names 
generally used are of lunar origin as given in § 5-7. 
These names are first found in the Taittirtya Safnhita 
7.4.8, and in many other places of the Yajur-Veda 
literature, but in a somewhat different form. We 
quote parts of the passage. 

Dual ; P = Plural. 

Taittirtya Safnhita, 7.4.8. 
Sarhvatsarasya yat phalguni purnamaso mukhata 
eva sarhvatsaramarabhya diksante tasyai kaiva 
nirya-yat sammedhye visuvant sampadyate 
Citra purnamaso dikseran mukharh va etat samvatsarasya 
yat citra purnamaso mukhata eva. . . 
Translation .—One should get consecrated on the 
■ Phalguni full-moon day because Phalgima full moon 
is the "mouth" of the year. Hence, ( such people ) are 



taken as consecrated from the very beginning of the 
year. But such people have to accept one 'nirya' 
(draw back), viz., that the 'Visuvan' occurs in 
the cloudly season ( sammedhya ). Hence, one should 
consecrate on the Citra full-moon day. The Citra full 
moon month is the *mouth J of the year. 

From these passages, we learn that the lunar month 
came gradually. The ancient Indians reckoned by 
the paksa or the fortnight, and distinguished the 
closing full moon day of the pak$a by the naksatra 
where the moon was full. Thus Phalguni Paurnamasi 
is that full moon when the moon gets full near the 
Uttara Phalguni star ( (3 Leonis \ one of the lunar 
mansions. Caitri Paurnamasi is that full moon, when 
the moon gets full near the Citra star ( a Virginis ), 
which is the 14th lunar mansion. Later, as the months 
were always full-moon ending, the word paurnamasi 
was dropped, and, e.g., the first part of Caitra- Paurna- 
masi, i.e., Caitra became the lunar month-name. The 
above passage says that the Phalguna Paurnamasi 
was regarded as the last day of the year and less 
frequently the Caitra Paurnamasi. This system still 
continues, and the first lunar month Caitra of the lunar 
year begins on the day after Phalguni Paurnamasi. 

There are twenty-seven naksatras and so only 12 
can be selected for lunar month-names. 

The twelve names which we have got are : 

Caitra from Citra (No. 14) 

Vaisakha „ Visakha ( „ 16) 

Jyai§tha „ Jyestha ( „ 18) 

Asa<}ha „ Asacjha ( „ 20 & 21 ) 

Sravana „ Sravana ( „ 22 ) 

Bhadra „ Bhadrapada ( „ 25 & 26 ) 

Asvina „ Asvini ( „ 1 ) 

Kartika „ Krttika ( „ 3 ) 

Margaslrsa „ Mrgasiras ( „ 5 ) 

Pausa „ Pusya ( „ 8 ) 

Magna „ Magha („ 10) 

Phalguna „ Phalguni ( „ 11 & 12) 

Of course, full moon takes place by turn in all 
the naksatras. But only 12 at approximately equal 
intervals could be selected. But we have too Rauhinya 
paurnamasi etc. the paksa when the moon becomes 
full near Rohini, or Aldebaran ( lunar mansion No. 4). 
But Rauhinya was not selected for the name of a 
lunar month, because it was too near Krttika- Paurna- 


'Tithi' or 'Lunar Day' is a very important concep- 
ition in Hindu astronomy, for holidays are always dated 
by the tithi. According to Siddhantic definition, a iiihi 

is completed when the moon is ahead of the sun by 
12°, or integral multiples of 12° ( vide § 57). 

Thus the first tithi ( Pratipada, lit. when the moon 
is regenerated ) in the waxing half starts when the 
moon is in conjunction with the sun, and ends when 
she has gone ahead of the sun by 12°, when the 
second tithi of the waxing moon begins. The tithis 
are numbered ordinally from 1 to 15, the end of the 
fifteenth tithi being full-moon. Then begins the 
tithis of the waning moon, numbered from 1 to 15, 
the end of the 15th tithi being the new-moon. There 
are thirty tithis in a lunar month, and though the 
average duration is less than a solar day, being 23,62 
hours, the length of individual tithis may vary from 
26.8 to 20.0 hours., on account of irregularity in the 
moon's motion. 

This is the definition of the tithi given in 
Siddhdntas or scientific astronomy which started about 
400 A. D. But this presupposes knowledge of measure- 
ment of angles, and precise scientific observation, of 
which we find no trace in the Vedic literature. What 
was then the origin of this system ? 

We have no reference to tithi in the Rg-Veda. 
The first reference is found in Yajurvedic literature, 
and the Brahmanas. The Taittiiiya Safnhitd talks of 
the pa%cadasi tithi, which shows that the lunar paksa 
was divided into 15 tithis, counted by ordinal numbers 
from 1 to 15 for each paksa. But what was the time- 
period meant by a tithi ? The Aitareya Brahmana 
attached to the Rg-Veda gives the following definition 
of the tithi. 

Aitareya Brahmana, 32.10 
Yam paryastamiyad abhyudiyaditi sa tithih. 
The tithi is that time-period about which the 
moon sets or rises. 

This has been interpreted by Prof. P. C. Sengupta 
as follows : 

During the waxing moon ( sukla paksa ), the tithi 
was reckoned from moon-set to moon-set ; and during 
the waning moon ( kfsna paksa ), the tithi was 
reckoned from moon-rise to moon-rise. The tithis 
were thus of unequal length, as shown by Prof. P. C. 
Sengupta in Table No. 11 on page 222. 


The history of the Indian calendar from the end 
of the Yajurveda period to the beginning of the 
Siddhanta Jyotisa period is very imperfectly known 
though there are plenty of calendaric references 
in the Brahmanas, Sutras, and the epic Mahahharata 
and various literature. On time-scale, it extends from 



Table 11. 
Duration of Vedic Tithi 


(1936 A.D.) 

Ending of Vedic Tithi 








Dvi tiya 

i ft 


C^.a 4-11 v^Vl 1 
wcu U Lll till 1 


Pq T"l/"»a TYlT 




Afl+QTYl 1 

















Pratipad & 








Pari cam I 


























Moonset or Sunset 


Time of Event 


Moonrise or 



(L. M. 




































Duration of 
Vedic Tithi 

18 18 

19 18 

20 20 

21 23 

22 23 

23 21 

24 14 

25 7 

25 58 

26 47 

27 37 

28 27 

29 17 

30 14 

17 15 




25 3 

24 40 

24 45 

24 50 

24 53 

24 55 

24 57 

24 58 

24 59 

11 33 

24 56 

24 58 

24 53 

24 53 

24 51 

24 49 

24 50 

24 50 

24 50 

24 57 

11 1 

24 45 

Vedic Elapsed 
Tithi No. 




Note : — The Vedic tithi ends 
when the moon remains invisible, 
tithis are of more than 24 hours' 

at moonset in the light half and at moonrise in the dark half. Near amavasya 
the ending is at sunset. There are 29 or 30 such tithis in a lunar month, and all 
duration except amavasya and purnima which are of about 12 hours' duration. 

an unknown antiquity, which is set by some at 1300 
B.C. to 300 A.D. 

The VeddTiga Jyotisa is generally assigned to this 
period. It may be said to be a sort of collection of 
short aphorisms giving mathematical rules for fixing 
the calendar in advance, and is known in three 
versions: the Rg-Jyotisa consisting of 36 verses, 
attached to the Rg-Veda and ascribed to one Lagadha 

as mentioned earlier, the Yajus Jyotisa attached to 
the Yajurveda and consisting of 43 verses, and there 
is a text ascribed to one Somakara, a commentator of 
unknown age of the Vedas. The dffferent texts 
contain about the same matter, but the verses are 
haphazardly arranged showing that the original texts 
have not come down to us in an unadulterated form. 
The number of independent verses in all the versions 



is not more than 49, and some of the verses have 
not been interpreted. 

There are several other calendarical treatises which 
can be assigned to this period. The Surya Prajnapli, 
a Jaina astronomical work, the Jyothakaranda, and 
the Kdlalokapralcasa. 

A short account of the calendaric rules followed 
in these treatises is given in Varahamihira's Paftca 
Siddhantika, Chap. XII, where the rules are collected 
as <% Paitdmaha Siddhanta" or Astronomical Calendar 
according to Grandfather Brahma, the Creator, in 
Hindu mythology. That shows the high antiquity of 
the rules. Varahamihira, as well as Brahmagupta 
describe the rules as very "inaccurate" {Duravibhrastau, 
furthest from truth in Varahamihira's language) though 
they pay a formal courtesy to the supposed authors. 
But such has been the case with calendars of all 
ancient nations, including the Babylonians at this 
period and a critical account of the Vedaiiga Jyotisa 
is important from the historical point of view. 

It may be remarked here that there are minor 
differences between Vedaiiga Jyotisa, the Jain systems, 
and the Paitamaha Siddhanta, which appear to be 
the latest of this group. The older treatises have a 
year of 366 days, while the Paitamaha Siddhanta has 
a year of 365*3569 days (Dlksit). 

There is an extensive literature on Vedaiiga Jyotisa 
^hich has been studied by Dr. G. Thibaut, S. B. Dlksit, 
;S. K. Pillai, and Dr. R. Shama Sastry, amongst others. 
We here give an account of the calendar according 
to the Paitamaha Siddhanta. 

Summary of the Contents 

"Five years constitute a Yuga or Saros of the sun 
and the moon. 

The yuga comprises 1830 savana days (civil days) 
and 1860 tithis (lunar days). 

In the yuga, there are 62 lunar months and 60 solar 
months. So two months are omitted as intercalary 
months, in a period of 5 years. 

The number of omitted tithis in the period 
is 30. 

There are 67 naksatra-months (sidereal months) in 
the yuga. The moon passes through 67x27 = 1809 
naksatras within this period. 

The yuga begins at winter solstice with the sun, 
and the moon together at the Bham-siha asterism 
(< or j3 Delphini)" 

These are the main points from which the five 
yearly calendar can be constructed. 

The Vedaiiga Jyotisa further describes measure- 
ments of the subdivisions of the day by means of the 
clepsydra, as well as by gnomon- shadows. 

One particular feature is the assumption that the 
ratio of the length of.ifche day to that of the night on 
the summer solstice day^rs as 3 : 2. 

Let us now examine these points critically. 

We observe that all the mathematical rules point 
out only to mean motions of the sun and the moon, i.e , 
the periods of the sun and the moon were obtained by 
counting the number of savana days in a large number 
of years and months, and dividing the number by the 
number of periods (year or month). No evidence is 
found of the systematic cfay to day observations of 
the sun and the moon. Only the lunar zodiac was 
used for describing the positions of the sun and the 
moon, which appears to have been divided into 27 
equal parts or naksatras ; in other words the naksatras 
no longer denoted star-clusters but equal divisions of 
the lunar belt. 

There is no mention of the zodiac or twelve signs 
of the zodiac, or of week days, or of planetary motion. 

Let us now look critically into the rules. 
5 solar years = 365.2422 x 5 = 1826.2110 days ; 

62 synodic months = 29 .53059 x 62 = 1830.8965 days ; 

67 sidereal months = 27.32166x67 -1830.5512 days. 

Therefore, regarded as a measure for luni-solar 
adjustment, the error is 4.685 days in a period of 5 
years, i.e., if we started a yuga with the sun and the 
moon together on the winter solstice day, the 
beginning of the next yuga (6th year) would occur 4.685 
days later than the winter solstice and in 5 to 6 yugas 
the discrepancy would amount to a month or half 
season. This cannot escape notice, and therefore 
there must have been some way of bringing back the 
yuga to the winter solstice day. Otherwise the calendar 
becomes useless. But how could it have been 
done ? 

This is a matter for conjecture and several 
hypotheses have been proposed. According to S. B. 
Dlksit, we should have in 95 years : 

according to the F. J.,f x 95 = 38 intercalary months, 
while actually we have, T \ x 95 = 35 intercalary months. 

So the Verfanga Jyotisa rules introduce 3 more 
intercalary months than necessary in 95 years, and if 
these are dropped, we can have good adjustment. This 
could have been done as follows : 

In the first period of 30 years = 6 yugas, suppose 
they had 11 intercalary months instead of 12. 

The beginning of the yuga would go ahead of the 
winter solstice in 30 years by 4'685 x 6 -28.110 days. 



But if we do not have the intercalary month on the 
30th year, the s/wgcr-beginning is brought back to 
29.53-28.110^1.421 days before the W.S. day. The 
same process is repeated for the next period of 30 
years. The ?/wga-beginning is thus brought back to 
2.842 days before the W.S. day. 

The next period may be taken to consist of 35 
years, i.e., 7 yttgas each of five years, in which the yuga- 
beginning goes ahead by 3.264 days. The combined 
result of the three periods of 30, 30, and 35 years is to 
put the yuga beginning ahead of the W.S. day by 0.422 
days only. Other conjectural cycles are described by 
Dr. Shama Sastry. 

But was any such practice really followed ? We 
have no evidence from the verses ; but S. B. Dlksit 
mentions that intercalary months were inserted only 
when needed, and hence probably they were 'dropped 
when not needed. 1 


The main object of the Vedaiiga Jyotisa calendar 
appears to have been the correct prediction of the 
tithi and nalcsatra on any savana (civil) day within the 
yuga. In this respect, the rules were more accurate. 
A tithi is defined as /^th of the lunar month. The 
correct measure is 

! uthi = ^0588 = 984353 daySi 

while the measure taken = .983871 days. The 
mistake is .000482 days on the lower side or one tithi 
in 2075 days or in 5f years. 

The five yearly period consists of 1830 civil days 
in which there are 62 synodical months. 

We know 62x29.53059 = 1830.8965 days. Hence 
in order to make the tithi calculations correct, one day 
(exactly 0.8965 days) had to be added to the total 
number of civil days in the period. 


The days were named according to the naksatras or 
lunar astensms in which the moon was found, and a 
lot of crude astrology* had grown up round this 
system. So it was necessary to predict the naksatra 
in advance. The Vedanga Jyotixa calendar prescribed 
some methods for such predictions. 

In a five yearly period of 1830 days, the sidereal 
revolutions of the moon amounted to 67 in which 
there are 1809 aak^ntras* 

Actually 1 naksatm day - 27 'g 166 = 1 .011913 days, 

while the measure taken = H§§ = 1.011608 days. 

♦Astrology based only on the sun and the moon. Later post- 
Siddhantic astrology in India is largely (J race o- Chaldean, and makes 
use of the si^ns of the -zodiac, and of planetary position and motion. 

The mistake was .000305 days on the lower side or 
1 naksatra in 3279 days or about 9 years. 

The Time of the Vedanga Jyotisha 

All recensions of the Veglanga Jyotisa contain the 
following verses : 

Svarakramete somarkau yada sakarii savasavau 
Syatfcadadiyugam maghastapah suklo'yanarh hyudak. (6) 
Prapadyete sravisthadau suryacandramasavudak 
Sarpardhe daksiiiarkastu maghasravanayoh sada. (7) 

These two verses taken together yield the following : 
The winter solstice took place at the lunar 
asterism &mm\ha, which is later called Dhani$\ha\. 

This is the 21st naksatra in the Kfitikadi system 
and 23rd in the Asvinyadi system and its component 
stars are a, 0, y and 8 DelphinL* These stars are far 
away from the ecliptic. We have for 1950 : 

a Delphini, Long. = 316° 41' Lat. -+33° 2' 

p m „ =315 39 y) -+31 55 

y „ -318 40 n =+32 41 

a „ „ -318 35 „ =+31 57 

The Arabs have and i Aquarii which also 
represent the Chinese Hsiu. 

It has been stated in the Vedaiiga Jyoii$a that the 
junction star of the asterism was placed at the 
beginning of the division and it marked the beginning 
of Uttarayana or the W.S. day. Thus the star 
representing the Dhani§thd division had 270° as the 
longitude at the time when the tradition of the Vedaiiga 
Jyotisa calendar was formulated. If a Delphini is taken 
as the principal star of the asterism, then its longitude 
was 270° at the time of the Vedaiiga Jyotisa and in 1950, 
its longitude is 316° 41'. As the solstices take about 
72 years to retrograde through one degree, the time of 
Vedanga Jyotisa is found to be (316° 41'— 270°) x 72- 
46 °7 x72 = 3362 years before 1950 A.D. or 1413 B.C. 
The star Delphini, however, yields a somewhat lower 
period, i.e., about 1338 B.C. 

The Plan of the Calendar 

In a period of 5 years, there are :— 
1830 civil days, 

62 lunar months, and so 1860 tithis, 
67 sidereal months and so 1809 nak§atras. 
As the period contains 60 solar months, there are 
2 intercalary months which are placed after every 

* On a Dhani?tha day the moon got conjoined with both the 
j3 and a Delphinis at interval of 2 hours. 



30 lunar months. Thus in the third year, the month 
Sravana is adhika which is followed by Buddha 
&ravana ; and in the fifth year the last month is also 
adhika which is adhika Magha, 

There are 1860 tithis while the number of civil 
days is 1830 ; so there are 30 omitted tithis {tithi ksaya). 
Each period of 61 days contains 62 tithis, so one tithi 
is omitted after 61 civil days. From this consideration 
the number of civil days per month can be obtained 
and will be shown in the table below. The Vedahga 
Jyotisa people regularly counted a tithi to a day, but 
after 61 days one tithi was omitted. 

As regards naksatras, their number is 1809 in 1830 
civil days, the difference being 21. So 87^ days weie 
equivalent to 86y naksatras. They counted a naksatra 
to a day successively, but after every 87 days (actually 
87y days), one naksatra was repeated for two days. 

The five different years of the period had 
distinctive names, vi%., (1) Samvatsara, (2) Parivatsara, 
(3) Idavatsara, (4) Anuvatsara, and (5) Idvatsara. 

The plan of the five yearly calendar is shown 
below : 

Table 12. 

Number of days in each month of the Vedanga 
Jyotisa Calendar 

Sain vat- 










Magha 30 





Phalguna 30 





Caitra 29 





Vaisakha 30 





Jyais^ha 29 





Asadha 30 





$ravana {adhika) — 


^ravana 29 





Bhadrapada 30 





Asvina 29 





Kartika 30 





Margasirsa 29 





Pausa 30 





Magha {adhika) — 

29 or 30 

Total No. of 355 





days in the year 



As already shown, the actual length of 62 lunar 
months is 1830.8965 days, while there are 1830 civil 
days in the five yearly period. It is therefore very 
likely that one civil day was added to the period 
when necessary to make it conform to the phases of 
the moon which were regularly observed. This 
additional day was no doubt placed at the end of the 

period, and when it was added the last month adhika 
Magha contained 30 days instead of 29 days which was 
otherwise its due. 

The ratio 1 for the duration of the longest day to 
that of the shortest night given in the Vedahga Jyotisa 
was first noted by Dr. Thibaut. Later the same ratio 
was found by Father Kugler from Babylonian cunei- 
form records of the Seleucidean period. The ratio is 
characteristic of a latitude of 35° N, which is nearly 
that of Babylon (for Babylon <p =32° 40'N). Hence it 
has been inferred that the Vedahga Jyotisa-asttoxiomzTS 
got this ratio from Seleucidean Babylon. But it may 
be pointed out that the Vedic life centred round 
North- Western India, from the SarasvatI valley 
(Kuruksetra 0=29° 55') to Gandhar (^31° 32'N). 
The ratios of the duration of daylight to night on the 
summer-solstice day for different latitudes are as 
follows : 

Table 13. 

Longest day and shortest night 

(Calculated with obliquity of ecliptic as 23° 51' vhiqji is 
for 1300 B. C. The results for 500 B. C. are also almost tha 


Longest day 

Shortest night 


30° N 

13 h 58 m 

10 b 2 m 


31° N 

14 3 

9 57 


31° 32' N 

14 6 

9 54 


32° N 

14 8 

9 52 


32°40' N 

14 12 

9 48 


33° N 

14 14 

9 46 


34° N 

14 19 

9 41 


35° N 

14 24 

9 36 


It is seen from the above table, that even at the 
latitude of Babylon, the ratio is not 1.50 but 1.45. At 
Gandhar, it is 1.42. The difference is not very large. 
But there is another factor to which attention must 
be drawn. 

Both Babylonians and Indians measured subdivisions 
of the day by means of some kind of Clepsydra. A 
description of the Clepsydra used by Indians during 
the Ved&nga Jyotisa-petiod will be found in S.B. Dlksit*s 
Bharatiya Jyoti&dtstra (Sec. II, Chap. I). But the day- 
length must have been measured from the observed 
time of sunrise to the observed time of sunset. This is 
somewhat larger than the astronomical time of sunrise 
on account of refraction. Assuming that the effect of 
refraction is to elevate a celestial body near the horizon 
by about 35', and the sun's semi-diameter is about 16', 
the sun's upper limb appears on the horizon at a place 
on 32° latitude, about 4 J minutes before the centre of 
the sun is due on the horizon. For the same reason, 
the sunset takes place 4£ minutes after the astronomical 



calculated sunset. So the apparent length of the day 
is increased by 2 x min. or by 9 minutes. Therefore 
for the latitude of Babylon we have the length of 
maximum day-light 14 h l2 m + 9- = 14 h 21 m , and the 
night is 9 h 39 m . The ratio is now 1.49. Taking the 
effect of refraction into consideration the ratio for 
Gandhar also becomes 1.46, which is not much 
different from 1.50 as for Babylon. So it is not 
necessary to assume that the ratio was obtained from 
Babylonian sources. 

Effect of Precession 

The Vedaiiga Jyotisa was prevalent for a long time 
over India, for over 1300 years (1000 B.C. to 300 A. D.). 
Hence it is likely that the subsequent astronomers 
noticed the gradual shift of the solstitial colure in the 
lunar zodiac. In fact, several references are found to 
this effect. Garga, an astronomer whose name is 
found in the Mahabharata, where he is described as 
having an astronomical school at a place called 
Gargasrota in the Sarasvatl basin, is the reputed author 
of a pre-Siddhantic calendaric treatise called Oarga 
Sainhita. He notes : 

Yada mvartate'praptal.i sravisthamuttarayane 

Aslesam daksine'praptab tada vindyanmaHad bhayam. 

Translation : When at the time of Uttarayana 
the sun is found turning (north) without reaching the 
Sravisthas, and (at the time of Bahsinayana) turning 
(south) without reaching the Mlesa, it should be 
taken to indicate a period of calamity. 

It shows that at the time of Garga the W.S. did 
no longer occur in &ravis\ha, neither the S.S. occurred 
in the Aslesa division. At the time of Vedaiiga Jyotisa 
the two solstices were marked by the starting point of 
&ravistha and the middle point of Mlesa respectively. 
Garga therefore observed that the solstices were reced- 
ing back over the lunar calendar, and had shifted at 
least by half a na/c$a*ra-division from the middle of 
A&lesa. His observations are therefore at least 480 
years labst'than those of the Vedaiiga Jyotisa. 

In the MaMbharata we get the following verse : 

Asvamedha, Chap. 44,2 
Ahal.i purvam tatoratrirmasah sukladayali smytali 
Sravanadini rksani rtavab sisiradayali 

Translation : Day comes first and then the night ; 
months are known to commence with the bright 
half, the naksatras with fcrpvana* and the seasons 
with &iiira. 

Here the asterism &ravana is described as the one 
where the winter solstice takes place. Sravana is 
just preceding &rav%8\ha and the solstices take about 
960 years to retrograde through one naksaira division. 

We get from this the time of composition of the 
Mahabharata as about 450 B.C. or sometime earlier. 

Varahamihira also notes that the winter solstice 
no longer took place at Bhanis\ha, 

PaHca SiddMntika, III, 21 
A slesardhadaslt yada nivrttih kilosnakiranasya 
Yuktamayanaih tadasife sampratamayanam 


Translation : When the return of the sun towards 
the south ( i.e., the summer solstice ) took place from 
the middle of Aslesa, the ay ana was right : at the 
present time ayana begins from Funarvasu. 

In his Bvhat Safnhita, an astrological treatise, he 
records : 

Bfhat Safnhita, . Ill, 1 

Aslesardhatdaksinam uttaramayanam raverdbaniflthadyam 
Nunam kadacidasit yenoktam purvasastresu. 

Translation : The beginning of the southern motion 
when the sun has passed half of Aslesa and the begin- 
ning of the northern motion when the sun has passed 
the beginning of Bhanis\ha, must have taken place 
at some epoch ; for these are recorded in old treatises. 

From the time of Vedaiiga Jyotisa to Varahamihira's 
time the summer solstice moved through more than 1| 
naksatras { i of Aslesa + Fusya ) which indicated a lapse 
of more than 1500 years from the time of Vedaiiga 

It is thus seen that the Hindu astronomers observed 
the shifting of the cardinal points due to precession 
of the equinoxes ; but as they had not developed the 
sense of era, they were unable to find out the time- 
interval between different records, and obtain a rate 
for precession, as was done by Hipparchos. Their 
observations were also crude, as they used only the 
lunar zodiac. The shifting of the solstitial colures 
remained to them an unsolved mystery. 


In this chapter, we are undertaking a critical 
review of the references to the calendar in ancient 
inscriptions, because, from the point of view of 
accurate history, inscriptional records are far more 
valuable than any references in ancient scriptures or 
classics, as they are contemporary documents, which 
have remained unaltered since the framers left them*. 

* Sometimes inscriptions and copper plate records have been 
found to have been forged at a latter date but such instances are 
rare and can not escape detection by an experienced archaeologist 



References in ancient scriptures, poems, epics and 
other literatures are, on the other hand, very often 
liable to alterations, interpolations and errors in the 
hands of latter-day copyists and are, therefore, less 

The oldest inscriptional records bearing a date 
( barring those belonging to the Ind^is-valley period 
which have not been deciphered ) belong to the reign 
of the Emperor Asoka ( 273-236 B.C. ). From these, 
wc can make fairly accurate deductions regarding the 
calendar then in use. 

We take the Fifth Pillar Edict, Rampurva version 
found at the Champarai) district, Bihar. The 
language is Asokan Prakrt, the script is the oldest 
form of Brahmi. ( Sircar pp, 62-63 ) 

Fifth Pillar Edict — Rampurva Version 

(1) Sadtmsatilva2mbhisitena(Sadv^ 

ktena) — * After twenty-six years had elapsed 
since coronation'. 

(2) Ti&u cdtufnmdlsl^u tisyafn pufnnamdsiyarn tint- 

divasdni cdvudasafn painnadasafn 2>atipadafn 

( Tisrsu cdtunndsisu tisydydfti pur^amdsydfn, 

trisu divasenu-caturdase pancadase pratipadi 

'On the three cdturmdsl days, on the tisya full 

moon day, on the 14th, 15th and the first 
day ' 

( On these and some other days, sale of fish is 

Again, in the same : 

(3) Athami-pakhdye cdvudasdye painnadawye 

tisd ye pundvasune (Astami-pakse, 

catur-dahjdfn, paftcadasydfn, tixydyd/n, 
punarvasau ) j 

'On the eighth paksa, on the 14th, and the 
15th ( new moon ) on the Tisya and 
Pimarvasu NaJcsatra days , 

(On these days, he forbids the castration of 

From these passages, we conclude that : 
1. , No era was used, but regnal years ( number of 
years elapsed since the king's coronation ) 
were used for dating. 

2. The time-reckoning was by seasons, each of 
8 paksas. The seasons are : 

Grlsrna (Summer) : Comprising Caitra, Vaisdkha, 

Jyai$tha, A$a4ha. 
Var$a (Rains) : Comprising Srdvaya, Bhddra, 

Asvina, Kartika. 
Hemanta (Winter) : Comprising Agrahayana, 

Pausa, Magha, Phdlguna. 

3. The months are not mentioned by name, except 
in one case where the month of Magha is 
mentioned. They are purnimditta, i.e., they 
started after full moon and ended in full moon. 
This is not expressly mentioned but can be 
inferred from the fact that the 14th, the 15th 
(PaTicadasi) and the Pratipada, i.e., the first 
tithi arc enjoined to be the days on which 
certain actions are forbidden. These must be 
the three days of invisibility of the moon, the 
14th being before new moon, the 15th the 
new moon, and the first, the day after new 
moon, which were observed as unsuitable for 
many particular performances. 
4. The day reckoning was by the tithi (lunar day), 
but the word tithi is probably not to be taken 
in the sense of the present Siddhantlc tithi, 
but in the sense of the Vedanga Jyotisa 
tithi or the old Brahmanic tithi. In the latter 
system, a tithi was counted from moon-set 
to moon- set during the bright half, and from 
moon-rise to moon-rise during the dark-half. 
There was the same tithi for the whole day. 
Prof. P. C. Sen Gupta has discussed this 
method of tithi reckoning ( see p. 222 ). 

5. Two days are mentioned by the lunar asterisms 
Tisya (<s Cancri), and Punarvasu (/3 Geminonon), 
As suggested one was probably his birth 
naksatm, the other his coronation tmkmtra. 
The days were therefore also named after the 
naksatra. This system is found in vogue in 
the epic Mahabhdrata, e.g., in the following 
passage : 

Balarama, the elder brother of Krsna, after returning 
from pilgrimage on the eighteenth day of the battle 
states : 

M. Bh., Salya Parra, Ch. 34, 6 

CatvariiiiHadalianyadya dve ca me nii.isi'tasya vai 
Pusyena saihpraySfco'smi Sravane punaragafcah. 
Translation : It is forty-two days since I left the 

house. I started on the Pusya (day) and have returned 

on the Sravana. 

6. There is no mention of the year-beginning. 
The Tisya Purnamasu i.e., the full-moon day 
ending the lunar month of Paw$a is marked 
out particularly. 

It appears from the records that in Asoka's time, 
the principles followed in framing the calendar were 
those given in the Vedafiga Jyotisa. No era was used. 
From the inscriptions, we can make no inference about 
the luni-solar adjustment, but there is no doubt that 
the year was seasonal as given in the inscription of the 
Satavahanas (see next page). 

a R.— 37 



No records bearing a date of the imperial dynasties 
following the Mauryas, the Sungas, and Kanvas 
(186B.C.-45 A.D.) are known. But the next imperial 
dynasty, the Satavahanas have left plenty of dated 
records. In these, the same system of date-recording 
by regnal years, the seasons, the paksas, and Uthis are 
found. There are 8 pak,as in a season of four months, 
and they were serially numbered from 1 to 8. The 
odd ones were KfW paksas, the even ones bukla 

Some examples are given below : 
(1) Nasik Inscription of the Satavahana Emperor, 
Gautamiputra Sri Satakarni (Sircar, pp. 192-93). 

Data paiika Savachare 10 + 8 vasapakhe 2 dimse 1 
(datta pa\tika Sar'nvatsare a^Uase 18 Varsapakse 
divtiye 2 divase prathame 1). 
i c the inscription was recorded in the eighteenth 
year elapsed since the coronation on the first day 
of the second Pak$a of the Vam season, i.e., in the 
lunar month of Sravaw> on the first day after new 
moon (&ukla pak$a). 

There are other Satavahana inscriptions similarly 
dated as summarized in the table below : 

Table 14. 

Table of Inscriptions of Satavahana Kings, 
showing date-recording. 


1024 Ratio Gotamiputasa Sami-Siriyaiia- 

Satakanisa ^ 16_G 1-5 

1100 Ba5o Vasithiputaaa Sami-Sm-Pulumavisa 7-G 5-1 
1106 R. V. Siri-Pulumavisa ■■■ 2 ^-H 3-2 

1122 B. V. Siri-Pulumayisa . •-• < >G 

1123 R. V. Siri-Pulumayisa •■■ iy "^ 

1124 R. V. Siri-Pulumavisa ••■ u-vi^-i* 

22-G 1-7 

1126 R. G. Satakanisa ^ 24 "^ A ' 6 

1146 R. G. Sami Siriyatia Satakanisa ... 7-H 

1147 R. y. Sami Siri-Pulumaisa ... 2 ' H 8 
90 (Sircar )- Siri-Pulumavisa ... 8 " H 2 ' 1 

B means ratio, V-Vasithiputasa, G -Gotamiputasa. 
The number in the first column indicates the serial 
number of the inscription in Lliders list. The last 
column contains dates, in an abridged form ; e.g., in 
1123, we have 19, G 2-13. Here 19' is the regnal year, 
G denotes Orima or summer season, *2' following G 
denotes the second prim i.e., the second half of the 
month of Caitra, constituting the &ukla pak$a, and the 
last numeral 13' denotes the day. But it is not clear 
whether the day is the lunar day, i.e., the tithi or the 
solar day. Even if it be the tithi, it is probably not 
the Siddhantic tithi, but the old Brahmanic or Vedafiga 

According to our calculations, the date of Gautami- 
putra Satakarni would be about the first century A.D. 
We take some still later records. 

(2) Raja Vlrapuru§adattaof Nagarjunlkon4a (Sircar, 

pp. 220-221) 

llainTto Siri VirapurisadaUw Sava d va pa 6 di 10 
(Rajnuh &rt<latta*ya safnvaisme 
msthe a varsapalse sasihe (> divase damme 10, 
On the sixth year of King Sri Virapuru§adatta on 
the 6th pah-va of the rarsa season, on the tenth day. 
The sixth of var*a pakta is month of Ssvina, second or 
light half (Sulda paksa). 

It is obvious from the above inscriptional evidences, 
that continuous era-recording was not used by Indian 
dynasts up to the time of the Satavahanas, and no 
ancient books, not even the Mahabharata mentions 
an era. 

As no era is mentioned, it has been difficult to work 
out a chronology of the early Indian dynasts including 
the Satavahanas. 

The Coming of the Era to India 

As we have seen in § 3.5, the era reckoning had been 
in use in Babylon since 747 B.C., and the Seleucidean 
era which marked the accession to power ot Selcucus 
at Babylon in 312 B.C., was widely current m the 
whole of the Middle East, both by the royalty and 
the public. 

But though as Asoka's Girnar inscription says that 
he was in diplomatic correspondence with five Greek 
kings of the West, including Antiochus I and II of 
Babylon, and the Ptolemy of Egypt, and sent Buddhist 
missionaries to these countries, it is clear from his 
records that he continued to use the purely Indian 
methods of date-recording based on the Vedaiiga-Jyotw* 
There is not the slightest indication that any of the 
Indian imperial dynasties which followed the Mauryas, 
ti*, the Sungas and Kanvas (186 B.C. -45 A.D.). the 
Satavahanas ( 100 A.D.) allowed themselves to be 
influenced by the Graeco-Chaldean luni-solar calendar 
which was then in vogue in the Near East. 

From about 180 B.C., North-Western India having 
Taxila as capital passed under the Bactrian Greeks. 

It is rather strange that though we have plenty of 
coins of the Bactrian Greeks who ruled in Afghanistan 
and N.W. India between 160 B.C., and 50 B.C., from 
which their names have been recovered, and some 
kind of chronology has been worked out, not a single 
record has yet been discovered which bears a date, 
except two doubtful ones. One is the coin of a 
certain Plato, found in the Kabul valley, which bears 
certain symbols which have been interpreted as 147 
of the Seleucidean era, i.e., 165 B.C., Plato has been 



identified by Tarn to be a brother of Eucratidas, 
founder of the second Greek ruling house (175 B.C.- 
139 B.C.) in Bactria. But the interpretation is 

The second one is an inscription of the time of 
king Menander, the great king of the Euthydemid 
house who ruled over the Punjab, Sind and Rajputana 
about 150 B.C., on the Shinkot Steatite Casket, the 
only one of the Greek kings who has found a 
permanent place in Indian literature in the celebrated 
Milinda Pafhho, a philosophical treatise meaning 
questions of king Menander. The inscription referred 
to mentions regnal year 5, the Indian month of 
Vaisakha, and the twenty-fifth day. Thus the date- 
recording is Indian, but slightly different from the 
system used in Asokan or Satavahana inscriptions 
because the. paksa is omitted. 

Our studies gi ven in § 3 3, shows that a mathe- 
matically accurate luni-solar calendar, based on 
astronomical knowledge, was first evolved in Seleucid 
Babylon between 300 B.C. to 200 B.C. by Chaldean 
astronomers. The features of this calendar were : 

(a) The use of the Seleucidean era for numbering 
years in place of the regnal years. 

(b) The beginning of the year with the lunar month 
.of Nisan which was to start on a date not later than 

a month of the vernal eqxinox. 

(This corresponds to the Indian month of Vaisakha 
later defined in Siddhantic calendars). 

(c) There was an alternative method of starting with 
the Greek month of Dios which was to begin on a 
date not later than a month of the autumnal equinox. 

(This corresponds to the Indian month of Kartika, 
as later defined in Siddhantic calendars). 

(d) Luni-solar adjustment was done by the nineteen- 
year cycle (vide § 3*2 — 3'4). 

This system of date-recording spread far and wide 
in the Near East and was adopted by other ruling 
dynasties, viz., the Parthians, who however used an era 
starting from 248 B.C. They used Macedonian months 
without alteration. 

I* can now be shown that this system penetrated 
gradually into India. 

Era or eras of unknown origin began to be 
mentioned in certain inscriptions found in the North- 
Western Punjab and the Kabul valley about the first 
century B.C. Some of them mention kings belonging to 
the Saka tribes who ruled Ariana (west and southern 
Afghanistan comprising the Herat regions-Area), the 
Kandahar regions (Arachosia), and Gandhara (N.W. 
Punjab) between the second century B.C. and the first 

century A.D. The inscriptions are mostly in Kharo'sthl 
and later ones found on Indian soil are in Brahml. The 
Kharosthl inscriptions are collected by Dr.Sten Konow 
in his monumental work Cm*pus Inscriptionum 
Indicarum, Vol. II., Part I., and are reproduced below 
in Groups A and B. 

Group A is identical with Konow's A (with the 
omission of Nos. 20-23) and contains dates from year 
58 to 200. Group B, identica with Konow's B-Group, 
contains the inscriptions of Kusana period bearing 
dates of years between 3C0 and 400. 


1. Maira : [sain 

2. Sahdaur A : ra\_ja] no Damijadasa saka-sa. 


(Reading uncertain.) 

3 . Sahdaur B : [ maharayasa ? ] Ayasa sain .... 

4. Mansehra : . .aq[hasathi.... 

5. Fatehjang : sain V>\9 Prothavatasa masasa divase 

sodase 10. 

6. Taxila copper-plate : sainratsaraye athasatatimae 

78 maharayasa mahaintasa Mogasa Panemasa 
masasa divase pafneame 5 etayc purvaye. 

7. Mucai : vase ekasitimaye 8 I. 

8. Kala Sang : [sain 10i)\ Reading uncertain. 

9. Mount Banj : sainvatsaraye 102. 

10. Takht-i-Bahi : maharayasa Guduvharasa vasa 

26 safnvatsarae tisatimae 103 Vesakhasa 
masasa divase [praiha] »ne [di 1 atra pwria'] 
pak ne. 

11. Paja : safnvatsaraye ekadasa [*a»] timaye 111 

Sravanasa masasa di [m*] se painlcada^se 15. 

12. Kaldarra : vasa 113 Sravanasa 20. 

13. Marguz : [vase 1*~\17. 

14. Pan j tar : sain 122 Sravanasa masasa di praclhame 

1 maharayasa Ousanasa rajami. 

15. Taxila silver scroll : sa 130 ayasa Asa4asa 

masasa divase 15 isa divase . . maharajasa 
rajatirajasa devaputrasa Khttsanasa aroga\ 

16. Pesawar Museum, No. 20 : sain 108 Je\hamase 

divase pafneadase. 

17. Khalatse : sain 187 maharajasa Uvimaka [vthi~\ 


18. Taxila silver vase : ka 191 maharaja ibhrata 

Manigulasa putrasa^Jihonikasa Cvkhsasa 

19. Dewai : sain 200 Vesakhasa masasa divase 

athame 8 itra khavasa. 



The Method of Date Recording 

A record fully dated in Group A gives : 

The year of the era in figures and words ; though 
it does not give any particular designation to the era. 

The month, mostly in Sanskrit ; the day, by its 
ordinal number, e.g., No. 11, which means in the year 
111 on the 15th day of the month of Sravaria. 

The months are all in Sanskrit, except in No. 6, in 
which the month is in Greek (Panemos = Asatfha). No. 
6 alone of this group contains the rather mysterious 
phrase 'Etaye purvaye' which means, 'before these*. 
This phrase, the meaning of which is not clear, occurs 
in Kusana (Group B) and even in Gupta inscriptions. 

This method of dating is quite different from that 
of the contemporary Indian dynasts, viz., the 
Satavahanas, which mentioned regnal years, the season, 
the paksa, and then probably the old tithi or the lunar 
day. But it agrees with the method followed in 
contemporary Parthia, which mentions the year 
usually in the Seleucidean era, rarely in the Arsacid 
era, the name of the month in Greek, and the ordinal 
number of the day, which ranges from 1 to 30 (see 
Debevoise, 1938). From No. 10, it appears that 
whenever Indian months were used they were 
Purnwianta, following the classical Indian custom. 

Date of records of Group A 

None of the inscriptions of Group A appear to 
be 'Royal Records' but some contain names of kings, 
e.g., No, 6, which mentions a Maharaja Mahainta Moga, 
who is taken to be identical with a king whose coins 
have been found in large numbers in Gandhara. He 
calls himself 'Maues' in the Greek inscription on the 
obverse, and Moasa (i.e. of Moa) in Kharosthl on 
the reverse. The title given there usually is 
Maharajasa Eajatirajasa Mahafntasa. It is held that 
King Moga was Saka leader who starting from a base 
in Seistan or Arachosia, invaded Gandhara through the 
southern route, sailed up the Indus, and ousted the 
Greek rulers Archebius from Taxila, Artemidorus 
from Puskalavati and Telephos from Kapsa (Bachhofer, 
1936) and founded a large empire comprising parts of 
Afghanistan, Gandhara and the Punjab. 

He is generally held to have been a Saka, but some 
hold without sufficient reason that he was a Tarthian. 
He is the first of Indo-Scythian kings known to 
numismatics. He was followed by other Indo-Scythian 
kings in Gandhara; who are known from wide variety 
of coins issued, viz., Azes I, Azilises and Azes II. 
But there is no clear reference to them in these ins- 
criptions except the word 'Ayasa' in Nos. 10 and 15, 

which is supposed to stand for Azes. But this has 
been disputed- 

This series starts with the year 58, if Cunningham's 
reading of (1) with the additional reading of the king's 
name 'Moasa' is accepted. But even if we reject it, 
the series certainly starts with the year 68 in No. 5, 
and goes up to 136 at fairly small intervals, then to 
168, 187, 191, 200 containing names of rulers known 
from coins, viz., besides Maues above mentioned, 
Gondophernes (103 = 20 B.C.), some Kusana king (122 
= 1 B.C.), Devaputra Kusana (136 = 14 A.D.), Maharaj- 
bhrata Jehonika (191=69 A.D.). They are held to be 
dated in the same era, which is usually called "the Old 
Saka Era, shortly called O.S.E. But up to this time, 
there has been no unanimity amongst scholars about 
the starting date of the era used in inscriptions 
grouped under A. 

We now take the second group of inscriptions 
which are those of the Kusanas, who ruled in North 
India in the second century A-D. 

The Ku§ana Inscriptions after Kaniska : 

24. Kaniska casket : sain 1 ma[ harayasa ] 


25. Sui Vihar : maharajasya rajatiraja&ya devapu- 

trasya Kaniskasya safnvatsare ekadase sain 
11 Baisi{rn)kasya masas[ y ]a divase( in) 
athavise 28 1 [ ay a ] tra divase. 

26. Zeda : sain 11 Asa4asa masasa di 20 Utara- 

phagune isa kswnami murotiasa 

marjhakasa Kaniskasa rajami. 

27. Manikiala : saM 18 Kartiyasa majh [ e ] divase 

20 etra purvae maharajasa Kaneskasa. 

28. Box lid : sain 18 masye Arthamisiya sastehi 10 

is [ e ] ksunaftimri. 

29. Kurram : sain 20 masasa Avadunakasa di 20 

is [ e ] ksunainmi. 

30. Pesawar Museum, No. 21 ; maharajasa [Vajus] 

kasa sain [24 Jethasa*!] masasadi ise 


31. Hidda : sainvatsarae athaviinsatihi 28 masye 

Apelae sasiehi dasahi 10 is [ e ] ksunainmi, 

32. Sakardarra : sain 40 P [ r ~\o\havada$a masasa 

divas[ami~\ visami di 20 atra divasakale. 

33. Sra : maharajasa rajatirajasa devaputrasa kaisa- 

rasa Vajheskaputrasa Kaniskasa sainvatsarae 
ekacapar[ i )sa[ i ] sain 4 1 Jethasa masasa di 
25 is [e] divasaksuiiami. 

34. Wardak : sain 51 masy[ e ] Arthamisiya 

sastehi 15 imena ga<trigrena maharaja 

rajatiraja Eoveskasra agrabhagrae. 



35. Ui)4 : sain 61 Cetrasa mahasa divase athanii 

di S iia k§unami Purvaxa4e. 

36. Mamane Dheri : sain S9 Margasirasra masi 5 ise 


An incomplete date, makasa di 25, is further 
found in the Kaniza Dheri inscription. 

The second group Nos. 34-36 contains Kharosthi 
inscriptions of the Kusana kings after the first Kaniska. 
These and Kusana Brahmi inscriptions mention : 

Years from '1 to 9a the kings Kaniska I from 

Vajheska from 24-28, Kaniska II of the 

year 41> 
Huviska from 33-60, 
Vasudeva from 62-98 
The King's name and the titles are given in full, 
and in the genitive. The era is generally ascribed 
to the famous Kaniska as we have a record of his first 

Their method of date-recording is the same as in 
Group A, viz., ( see No. 25 ) the year of the era, the 
month name in Greek or Sanskrit, the ordinal number 
of the day* then the phrase equivalent to asyai'n 
purvayaM ( before these ), but in these inscriptions, 
it is expressed in the form ise kxunawi or its variant, 
which has been interpreted by Konow as equivalent 
of asyafn or etasijafn pUrvatjain in the Khotani Saka 
language which Konow thinks was the mother tongue 
of kings of the Kaniska group and which they use in 
their inscriptions. In fact kings of this group use 
a number of Khotani Saka words, and from their wide 
range of coins are known to have put in a medley 
of Greek, Iranian, and Indian gods including Buddha 
on their coins, but the names of the gods are not in 
their original Indian, Iranian or Greek form but invari- 
ably in the form used in the Khotani Saka language. 

The method of date-recording followed by the 
Kusanas, in spite of its identity with that of Group A 
shows some interesting variations. In the Kharosthi 
inscriptions of the Kusanas, the months are mostly 
Greek, less so in Sanskrit ( Caitra, Vaisdkha, etc. ). 
The days run from 1 to 30 and clearly they are not 
tithis but solar days. When we turn to Brahmi inscrip- 
tions, we find that the month names are mostly 
seasonal : Oiima, Var$d, or Hemanta as in the Satava- 
hana records. But since 4 is the maximum number 
attached to these, and the day numbers run from 
1 to 30, the number after the season denotes a month, 
not a pak$a and the days are solar. Thus G 4 denotes 
the fourth month of the Gri$ma season, viz, A$a<lha, 
and not the fourth pah$a as was the case with the 
SatavShanas which would be the second half of 
Vai&kha. The pak$a is given up. 

This is a deviation from Satavahana method of 
date-recording and follows closely the Graeco-Chal- 
dean method. Some inscriptions mention Greek 
months ( e. g. Gorpiaios which is Asvina or Bhadra 
in Sircar's No. 49, p. 146 ) others Indian lunar months 
( e. g. Srarana in No. 51 ), but their number is small 
compared with the seasonal mode of recording months. 
These inscriptions give no indication as to whether 
the month is Purijimanta or Amanita. The Indian 
months are Puruiviattta. 

But the Zeda inscription of year 11 ( No. 26 of 
Group B) mentions that the imhsatra was TJUaraphalgurd 
on the 20th of Asdiiha, and ( 35 ) mentions that in 
the year 61, the mikmtra on the 8th day of Caitra was 
Pnrvasadha. A comparison with tables of naksatra* 
shows that the months ended in full moon {Purr^imdnid). 
As purnimanta months were unknown outside India, 
the Kusanas must have yielded to Indian influence 
and adapted their original time-reckonings to the 
Indian custom; at least in their use of Indian months. 

Historians and chronologists now almost unani- 
mously hold that all these inscriptions of Group B are 
dated in the same era which is sometimes called the 
Kusana era, which was founded by King Kaniska. 
This is said to be proved by the fact that the inscrip- 
tions range from year 1, and we have phrases as in 
No. 25 of the Maharaja Bdjddhirdja Devaputra 
Kani$Jca, in the year 11. But a little more scrutiny 
shows that it is only a conventional phraseology, used 
in almost all Kusana inscriptions, for even in as late 
a^s an inscription of year 98 of this group, we read 'of 
the Maharaja Vasudeva in the year 98\ ' It is therefore 
by no means clear that such phrases can be interpreted 
to *nean that Kaniska started an entirely new era. 
In fact, from Kaniska s profuse use of Greek months 
and Greek gods, in his inscriptions and coins, 
Cunningham was led to the belief that Kaniska dated 
his inscriptions in the Seleucidean era, with hundreds 
omitted, so that year 1 of Kaniska, is the year 401 
of S. E. and year 90 of the Christian era. 

But it has been known for some time that the 
Kusana empire did not stop with that Vasudeva who 
comes after Huviska. Dr. L. Bachhofer (1936) has 
proved from numismatics the existence of : 

Kaniska III, reigning apparently after Vasudeva I, 
Vasudeva II, reigning after Kaniska III. 
The kings appear to -have retained full control of 
the whole of modern Afghanistan including Bactria 
which appears to have been the home land of the 
Kusanas and some parts of the Punjab, right up to 

There is yet no proof for or against the point that 
they retained the eastern parts, after year 98 of Kusana 



era. Herzfeld had established that Vasudeva II, 
who appears to have come after Kanaka III .about 
210 A.D., was deprived of Bactria by Ardeshir I, the 
founder of the Sasanid dynasty of 'Persia. The 
Sjsanids converted Bactria into a royalvprovince under 
the charge of the crown prince, who struck coins 
closely imitating those of the Kus5nas. Vasudeva II 
is also mentioned in the Armenian records of Moise of 
Khorene, a Jewish scholar, under the name Vehsadjan, 
as an Indian king who tried to form a league with 
Armenia and other older powers against the rising 
imperialism of Ardeshir. Vasudeva II is also thought 
to have sent an embassy to China about 230 A.D *. 

The second Sassanian king Shapur I, claims to have 
conquered sometime after 240 A.D. l PSKVR% which has 
been identified with Puru§apura or Peshawar, the 
capital of the KusSnas. This has also been confirmed 
by the French excavations at Begram (Kapi£i) in 
Afghanistan, which was destroyed by Shapur between 
242 and 250 A.D. But this probably was not a 
permanent occupation but a raid, as a Ku§ana king 
or Shah is mentioned in 'the Paikuli inscription of the 
Sasanid king Narseh (293-302 A.D.). 

Kushana Method of Date-recording In India : 

It appears rather strange that the Kusana way of 
date-recording should suddenly come to a dead stop 
on Indian soil with the year 98 of Vasudeva I, and no 
records containing a year number exceeding 100 should 
be found on Indian soil. 

The mystery appears now to have been successfully 
solved by Mrs. Van Lohuizen de Leeuw in her book 
The Scythian Period (pub. 1949). She has proved that 
several Biahml inscriptions in the Mathura region bear 
dates from years 5 to 57 in which, following an old 
Indian practice, the figure for hundred has been 
omitted. Thus k 5 T stands for 105, '14' stands for 114 
of the Kusana era. The following example will suffice 
(vide pp. 242-43 of the Scythian Period). 

Cue and the same person Arya Vasula, female 
pupil of Arya Sangamika, holding the important 
position of a religious preacher in the Jaina community, 
is mentioned in two Brahmi inscriptions (No. 24 and 
No. 70 of Lliders) bearing the year designations of 15 
and 86 respectively, the date-recording being in the 
typical Kusana style. The palaeographical evidence 
also shows that the inscriptions were recorded in the 
Kusana age, though the name of the reigning monarch 

* Ghirshman thought that the Viisudev* Kusana of these 
references is Vasudeva I, whose last reference is year 98. He equated 
year 98 of Kanaka's era to year 242-250 A.D., and arrived at the 
date 144 to 152 A.D. for the initial year of the Kanaka era. But the 
equation of this Vasudeva with Vasudeva I is certainly wrong. This 
must be Vasudeva II, or may be a still later Vasudeva. 

is not mentioned. Now it is clearly impossible that 
the same person would occupy such an important 
position from the year 15 to 86, a period of 71 years. 
L. de Leeuw therefore suggests that while 86 is the 
usual Ku$ana year (reckoning from year 1 of Kaniska), 
'15' is really with hundred omitted and represents 
actually the year 115 of Kaniska, i.e., dates of the two. 
inscriptions differ by 115-86 = 29 years, which is much 
more plausible. In other words, after the year 100 of 
the Kanaka era was passed, hundreds were dropped 
in inscriptions found near about Mathura. 

The author has sustained her ground by numerous 
other illustrations, and there seems to be no doubt 
that this is a brilliant suggestion and it can be taken 
as proved that in numbering years of an era, hundreds 
were omitted in certain parts of the Kusana dominion 
in the second century of the Kaniska era. L. de 
Leeuw has found such dates in no less than 7 instances 
bearing years 5, 12, 15, 22, 35, 50, 57 in which 
apparently 103 has been omitted, so that 57 really 
stands for 157, and if we take the Kaniska era to have 
started from 78 A.D., the date of the last one is A.D. 
235 = (157 + 78). Probably the name of the reigning 
king was not mentioned, as he had either lost 
control over these regions, or as the inscriptions were 
religious, it was not considered necessary. The second 
alternative appears to be more correct. 

This is supported by the inscription on an image 
discovered by Dayaram Sahni in Mathura in 1927. 
It mentions Maharaja Devaputra Kaniska. But on 
palaeographic grounds, he can neither he Kaniska I 
(1-24) nor Kani§ka II (41), but a later Kaniska, coming 
after Vasudeva I, and 14 is really year 114 of the 
Kaniska era. We may identify him with Kaniska 
III of Bachhofer. 

So we come to this conclusion : 

The records of Ku?ai)a kings, after Kaniska I 
range from year 1 to 98. In the second century of 
the Kaniska era, hundreds are omitted and such 
records have been found up to year 157, i.e., year 235 
of the Christian era. 

This raises a strong presumption that Kaniska 
was not the founder of the era, but he used one 
already in vogue, but omitted the hundreds. Thus 
year 1 of Kaniska is really year 1 plus some hundred, 
may be 1, 2, or 3. L. de Leeuw does not expressly 
suggest this, though it is apparent from her reasoning 
that year I of King Kaniska is year 201 of the Old &aka 
era*. If this suggestion be correct, since the old Saka 
era is taken to have started in 123 B.C. ( — 122 A.D.) 
instead of in 129 B.C., -as postulated by L. de Leeuw, 
Kaniska started reigning in ( 201-123 )«78 A.D. 

* The suggestion is of Prof. M. N. Saha. 



From the above review of inscriptional records and 
contemporary history, the following story has been 

(1) The Saka era was first started in 123 B.C. 
when the Sakas coming from Central Asia due to the 
pressure of HOnas wrested Bactria from the Parthian 
emperors after a seven years' war. The leader was 
probably one 'Azes', and therefore the era was also 
alternately called the 'Azes' era. This Azes is not to 
be confounded with the two later Azes who succeeded 
Maues and reigned between 45 B. C. to 20 B. C. 
Earlier Sakas used Macedonian months and Graeco- 
Chaidean method of date recording, prevalent 
throughout the whole of Near East. In Indian 
dominions, Indian months which were equated to 
Greek months were used. As their coins show, the 
xuling class had adopted Greek culture. / 

(2) When the Sakas spread from 'Sakasthan , i.e., 
modern Afghanistan into contiguous parts of India, 
they began to be influenced by Indian culture. During 
the first stage, they exclusively used Greek in their 
coins, but later they began to use Kharosthi and 
Brahml as well. The coins of Maues (80 B.C.-45 B.C.), 
Azes I, Azilises, Azes II show increasing influence 
of Indian culture. The southern Sakas who penetrated 
into Saurashtra and Malwa show Indian influence to 
a greater degree. 

(3) In the first three centuries, they (Maues group, 
Nahapana group and Kusanas) used the old Saka era 
-omitting hundreds, and using a method of date- 
recording which was an exact copy of the contem- 
porary Graeco-Chaldean system prevalent throughout 
the Parthian empire (Macedonian months, and 
ordinal number of days). But they also began to use 
Indian months. Whenever they did it, the month 
was Purnimania, as was the custom with old Hindu 
dynasts (Mauryas and Satavahanas). 

(4) The classical Saka era starting from 78 A.D. 
is nothing but the old Saka era, starting from 123 B.C. 
with 200 omitted, SO/ that the year 1 of Kaniska is 
year 201 of the Old Saka era. 

&aka Era in the South- West. 
Besides the earlier Sakas belonging to the Maues 
group, and the Kusanas, there was another groupof Saka 
kings, who penetrated into the south-western part of 
India! The earliest representative of this group was 
Nahapana and his son-in-law Usavadata. Their 
records are dated in years 41 to 46 of an unknown era. 
They use Indian lunar months and days (probably tithis). 
These Sakas ruled in Rajputana, Malwa, and northern 
Maharastra and were engaged in continuous warfare 
with the Satavahana ruler Gautamlputra Satakarni 
who claim to have destroyed them root and branch. 

The senior author has shown that Nahap3na used 
the old Saka era with one hundred omitted, so that 
the year 46 of Nahapana was the year 146 of the old 
Saka era or about 24 A.D. 

The Satavahana kings Gautamlputra Satakarni and 
his son Vasisthlputra Pulumavi, whose records are 
found dated in the typical Indian fashion, reigned 
according to his hypothesis from about 40 A.D. to 80 
A.D. From epigraphical record, Nahapana is at least 
separated by about 100 years from the next group of 
Saka rulers, the Sakas of U]jain belonging to 

the house of Castana, 

The Saka satraps of Ujjain. 
We come across the records of- another Saka ruling 
family, reigning in Ujjain. 

[Andau (Cutch) stone inscriptions of the time of 
Castana and Rudradaman, Sircar, p. 167]. 

Rajnah Castanasya Jdmotika-putrasya rajfiah Jludra- 
damnah Jaymldma-putrasya [ca] var$e diipaftcase 52 
Phalguna-bahulasya { = krsna-pak$asya) dvillya vare 
{^divase) 2 tnadanena Sifnhila-putrena bhaginyah 
Jyes thaviraya h Sifn hila-duhitu h aupasati sagotraya h 
yastih utthdpita- •• . 

Translation: Of king Castana, son of Jamotika 
and of king Rudradaman son of Jayadaman, in the year 
52, on the dark half of the month of Phalguna and on 
the 2nd day *' 

This inscription mentions the year 52, the second 
day of the Kfsna paksa of the month of Phalguna. 

There is no doubt that the year mentioned is that 
of the &aka era as now known. For this satrapal house 
reigned continuosly for nearly 300 years and has left a 
wealth of dated records. But the name of the era is 
not mentioned in the earlier records. They are 
mentioned merely as years so and so. ^ 

The earliest authentic instance of the use of Saka 
era by name is supplied by the Badami inscription of 
Calikya Vallabhesvara (Pulakesin I of the Calukya 
dynasty), dated 465 of the Saka era {&aka-Varsesu 
Catus-s-atesu paftca-sasthi-yutesu : Epigraphia Indica 
XXVII, p. 8J. In literature the use of the era by name 
appears still earlier. The Lokavibhaga of SimhasOri, a 
Digambara Jaina work in Sanskrit is stated in a 
manuscript to have been completed in 80 beyond 300 
(i.e. 380) of the Saka years (Ep. ImU XXVII, p. 5). 
There is no doubt that the era used in the records of 
the western satrapal house beginning with Castana 
and Rudradaman have come down to the present times 
as the Saka Era, which is the 'Era' par excellence 
used by Indian astronomers for purposes of calculation. 
There ere 30 or more 'Eras' which have been in use 
in India {vide § 5*8), but none of them have been 



used for calendarical calculation by the Indian 

astronomers. / 

Yet it is difficult to assign the origin of the Saka 
era to the western satraps. An era can be founded 
only by an imperial dynasty like the Seleucids, the 
Parthians or the Guptas. The western satraps never 
claim, in their numerous records, any imperial position. 
They are always satisfied with the subordinate titles 
like Ksatmpa {Satrap) or Maha Ksatrapa (Great Satrap) 
while the imperial position is claimed by their 
northern contemporaries, the Kusanas. 

The conclusion is that the western Ksatrapas 
used the old Saka era, with 200 omitted ; so that year 
1 of the present Saka era is year 201 of the old Saka 
era, i.e., (201— 122) = 79 A.D. 

The gradual adoption of characteristic Indian 
ideas by the Sakas is shown in a record of Satrap 
Rudrasimha dated 103 S.E. or 181 A.D. 

[Gunda Stone Inscription of the time of 
Rudrasimha I, Sircar, p. 176] 

Siddham. Rajnah mahdksatrapasya svdwi-Castana- 
prapautrastja rajnah kmtravasya svaml Jayaddmavaittrasya 
rajnah mahdksatrapasya srdmi-Rudraddma'Putrasya 
rajnah ksatrapasya svdmi-Rudrasifnhasya varse tryutta- 
ra&ata (tame) ( = adhika) 103 Vaisdkha snddhe 
( = suklapakse) paftcama-dhanya tithatt Rohint naksatra- 
muhurte abhirena senapati Bappakasya put rem senapati 
Rudrabhutind grame rasapadrake vapi ( = kvpah) 
khanita, bandhitd [stladibhih] ca sarva sattvanafn hita- 
mkharthaw iti. 

Translation : Of king Mahaksatrapa of Svaml 

Rudrasimha in the year 103 in the light half of the 
month of Vaisakha on the 5th tithi and in the Rohirji 
naksatra muhurta, 

The Saka satrap Rudrasimha, reigning in 181 A.D. 
thus dates his inscriptions using an era (the Saka era), 
purely Indian months, tithis and naksatras. This is 
in full Siddhantic style, because the characteristic 
features of Siddhantic method of date recording which 
mention ////// and naksatra are first found in this 
inscription. The 'week day' is however not mentioned. 

This is first mentioned in an inscription of the 
emperor Budhagupta (484 A. D.). 

Sate pauaiyixtyadhike varsauam bhupatau ca 
' Budhagupie Asddha rndsa [sukla~] — [f/m] dasyain 

(Iran- Stone Pillar Inscription of Bndha Gupta — 
Gupta year 165-484 A.D.). 

Translation ; In the year 165 of the Gupta era 
during the reign of emperor Budhagupta in the month 
of Asadha and on the 12th tithi of the light half which 
was a Thursday (i.e. day dedicated to the preceptor 
of Gods). 


Rise of Siddhantas or Scientific Astronomy 

The Vedahga Jyotisa calendarical rules appear, 
from inscriptional records, to have been used right up 
to the end of the reign of the SatavShanas (200 A.D.). 
The analysis of inscriptional data on methods of date- 
recording given in § 5*5 shows that it was the Saka 
and KusSna rulers (50 B.C. - 100 A.D.). who introduced 
the Graeco-Chaidean methods of date-recording,, 
prevalent in the Near East into India. These methods 
require a knowledge of the fundamentals of astronomy, 
which must have been available to the Saka and 
Kusana rulers. In India, as the inscriptional records 
show, some purely Indian dynasts probably accepted the 
system in full from about 248 A.D. (date of foundation 
of the Kalachuri era, the earliest era founded by Indian 
kings, leaving aside the Saka era which is admittedly'of 
foreign origin and the Vikrama era whose origin is still 
shrouded in mystery). During the time of the Guptas 
who founded an era commemorating their accession to 
power in 319 A.D. the integration of the western 
system with the Indian appears to have been complete. 

Indian astronomical treatises, explaining the rules 
of calendaric astronomy, are known as Siddhantas, but 
it is difficult to find out their dates. The earliest 
Indian astronomer who gave a date for himself was the 
celebrated Aryabhata who flourished in the ancient 
city of Pataliputra and was born in 476 A.D. 

It is necessary to reply to a question which has 
very often been asked, but never satisfactorily 
answered, vi,\., 

Why did the Indian savants who were in touch with 
the Greeks, and probably with Greek science since the time 
of Alexander's raid (323 B.C. \ take about 500-600 years 
to assimilate Greek astronomy, and use it for their own 
calendar- framing ? 

The Indians of 300 B.C. to 400 A.D., were quite 
vigorous in body as well as in intellect as is shown by 
their capacity to resist successive hordes of foreign 
invaders, and their remarkable contributions to 
religion, art, literature and certain sciences. Why did 
they ,not accept the fundamentals of Greek astronomy 
for calendarical calculations earlier ? 

The reply to this query appears to be as follows : 

The Greeks of Alexander's time had almost nothing 
to give to the Indians in calendaric astronomy, for 
their own knowledge of astronomy at this period was 
extremely crude and far inferior to that of the 
contemporary Chaldeans. The remarkable achieve- 
ments of the Greeks in astronomy, and geometry,. 



though they started from the time of Alexander 
(Plato's Academy), really flowered in full bloom in the 
century following Alexander (330 B.C. -200 B.C.). 
The culmination is found in. Hipparchos of Rhodes 
who flourished from 160—120 B.C. ; he wrote treatises 
on astronomy. Simultaneously in Seleucid Babylon, 
Chaldean and Greek astronomers made scientific 
contributions of the highest order to astronomy ( vide 
§ 4.7 & 4.8 ), but none of their works have survived, but 
are now being found by archaeological explorations. 

It is therefore obvious that the Indians of the age 
of Asoka (273 B.C.— 200 B.C.), who were in touch with 
the Greek kingdoms of Babylon and Egypt, had not 
much to learn from the Greeks in astronomy. 

The Mauryas were succeeded by the Suhgas 
(186 B.C.— 75 B.C.), but Indians during this age were in 
touch only with the Bactrian Greeks. But by this time, 
the Parthian empire had arisen (250 B.C.), producing 
a wedge between western and eastern Greeks. The 
only dated record of the Indo-Bactrian king, 
Menander (150 B.C.), is purely Indian in style. 

By about 150 B.C., direct contact between India 
and Greater Greece which included Babylon had almost 
ceased, due to the growth of the Parthian empire. 
Whatever ideas came, was through the Saka-Kusana 
kingdoms which came into existence after 90 B. C. By 
that time, astronomy was regarded as only secondary 
to planetary and horoscopic astrology, which had 
grown to mighty proportions in the West. This may 
have been probably one of the main reasons for late 
acceptance of Graeco-Chaldean astronomy in India, 
for Indian thought during these years ivas definitely 
hostile to astrology. 

It will surprise many of our readers to be told 
that astrology was not liked by Indian leaders of 
thought, which dominated Indian life during the period 
500 B.C.- 1 A. D. Nevertheless, it is a very correct 

The Great Buddha, Whose thoughts and ideas 
dominated India from 500 B.C. to the early centuries 
of the Christian era, was a determined foe of astro- 
logy. In Buddha's time, and for hundreds of years 
after Buddha, there was in India no elaborate planetary 
or horoscopic astrology, but a crude kind of astrology 
based on conjunctions of the moon with stars and 
on various kinds of omina such as appearance 
of comets, eclipses, etc. But Buddha appears to 
have held even such astrological forecasts in great 
contempt, as is evident from the following passage 
ascribed to him : 

Yatha va pan'eke bhonto, Samana-brahmana 
saddha-deyyani bhoianani bhurijitva te evarupaya 
tiracchana-vijjaya micchajivena-jibdkam kappenti- 

seyyathidam "canda-ggaho bhavissati, 
suriyaggaho bhavissati, nakkhatta-ggaho bhavissati. 
Candima suriyanarh pathagamanarh bhavissati, 
candima suriyanarh uppathagamanarh, bhavissati, 
nakkhattanam pathagamanam bhavissati, 
nakkhattanam uppathagamanarh bhavissati. 
Ukkapato bhavissati. Disa-daho bhavissati. 
Bhiimicalo bhavissati. Devadundubhi bhavissati. 
Candima suriya nakkhattanam uggamanam 
ogamajaam samkilesarh vodanam bhavissati."* 

(Digha Nikaya, Vol. 1, p. 68, Pali Text Book Society) 

Translation : Some brahmanas and §ramatyas earn 
their livelihood by taking to beastly professions and 
eating food brought to them out of fear ; they say : 
"there will be a solar eclipse, a lunar eclipse, occulta- 
tion of the stars, the sun and the moon will move in 
the correct direction, in the incorrect direction, the 
naksatras will move in the correct path, in the 
incorrect path, there will be precipitation of 
meteors, burning of the cardinal directions (?), earth- 
quakes, roar of heavenly war drums, the sun, the 
moon, and the stars will rise and set wrongly producing 
wide distress amongst all beings, etc." 

This attitude to astrology and astrolatry on the 
part of Indian leaders of thought during the period of 
500 B.C. to 100 A.D., was undoubtedly a correct one, 
and would be welcomed by rationalists of all ages and 
countries. But such ideas had apparently a very 
deterrent effect on the study of astronomy in India. 
Pursuit of astronomical knowledge was confused with 
astrology, and its cultivation was definitely forbidden 
in the thousands of monasteries which sprang all over 
the country within few hundred years of the Nirv5na 
(544 B.C./ 483 B.C). Yet monasteries were exactly the 
places where astronomical studies could be quietly 
pursued and monks were, on account of their leisure 
and temparament, eminently fitted for taking up such 
studies, as had happened later in Europe, where some 
of the most eminent astronomers came from the 
monkist ranks, e.g., Copernicus and Fabricius. 

Neither did Hindu leaders, opposed to Buddhism, 
encourage astrology and astrolatry. The practical 
politician thought that the practice of astrology was 
not conducive to the exercise of personal initiative 
and condemned it in no uncertain terms. In the 
Arthasa&tra of Kautilya, a treatise on statecraft, which 
took shape between 300 B.C. and 100 A.D., and is 
ascribed to Canakya, the following passage is 
found : 

* Acknowledgement is due to Prof. Mm. Bidhusekhar Sastri,. 
who supplied these passages. 

C. B. — 38 



Kautiliya Artha&astra 

Nakflatram atiprcchantam balam artho'tivartate 
Arfcho hyarthasya nakaatram kirii karisyanti tarakab. 

Translation : The objective (artha) eludes the 
foolish man {balam) who enquires too much from the 
stars. The objective should be the naksatra of the 
objective, of what avail are the stars ? 

This may be taken to represent the views of the 
practical politician about astrology and astrolatry, 
during the period 500 B.C. to 100 B.C. 

Canakya was the great minister of Candragupta, 
and history says that these two great leaders rolled 
back the hordes of the Macedonians, who had con- 
quered the Acheminid Empire of Iran comprising 
the whole of the Near East to the borders of Iran, 
and thereafter laid the foundation of the greatest 
empire India has ever seen. They clearly not only did 
not believe in astrology, but openly, and uithout reserve, 
ridiculed its pretensions. 

But the influence of original Buddhism waned after 
the rise of Mahayanist Buddhism, which received 
great encouragement during the reign of Kaniska 
<78 A.D. to 102 A,D.) and other Kusana and Saka 
kings. Then came Buddhist iconography, coins, and 
knowledge of the methods of western date-recording 
which the Sakas and Kusanas used. They blended 
with the indigenous Indian system slowly. 

The focus of diffusion of western astronomical 
knowledge appears to have been the city of UjjayinI, 
capital of the western Satraps who were apparently 
the first to use a continuous era ( the Saka era ), and 
a method of date-recording which was at first purely 
Graeco-Chaldean as prevalent in Seleucid Babylon, 
but gradually Indian elements like the tithi and the 
naksatra were blended, as we find for the first time 
in the inscription of Satrap Rudrasimha, dated 181 
A.D. t (vide§5-5). 

This city of Ujjayini was later adopted as the 
Indian Greenwich, for the measurement of longitudes 
of places. The borrowal of astronomical knowledge was 
not therefore from Greece direct, but as now becomes 
increasingly clearer, from the West, which included 
Seleucid Babylon, and probably through Arsacid 
Persia. The language of culture in these regions 
was Greek, and we therefore find Greek words like 
kendra (centre), lipiikd (lepton), hora (hour) in use by 
Indian astronomers. 

This view is supported by the Indian myth that 
astrolatry and astrology were brought to India by a 
party of Sakadvipi Brahmanas (Scythian Brahmins), 
who were invited to come to India for curing Samba, 
the son of Krsna, of leprosy by means of incantations 

to the Sungod. Professional astrologers, in many 
parts of India, admit to being descendants of these 
&ahadvipi Brahmanas and probably many of the 
eminent astronomers like Aryabhata and Varahamihira 
who made great scientfic contributions to astronomy 
belonged to this race. The planetary Sungod is always 
shown with high boots on, as in the case of Central 
Asian kings (e.g., Kaniska). 

It is a task for the historian to trace how the steps 
in which the importation of western astronomical 
knowledge took place for the Siddhantas, which 
incorporate this knowledge and are all a few centuries 
later, and many of them bear no date. 

A good point d y appui for discussion is Varahamihira's 
Pa%ca Siddhantikd ; for Varahamihira's date is known. 
He died in 587 A.D., in ripe old age so he must have 
written his book about 550 A.D. This is a compendium 
reviewing the knowledge contained in the five 
Siddhantas which were current at his time. These 
were regarded as 'Apauruseyd or "knowledge revealed 
by gods or mythical persons". 

The five Siddhantas are : 

Paitarnaha ♦••Ascribed to Grandfather Brahma. 

Vasistha •••Ascribed to the mythical sage 
Vasistha, a Vedic patriarch, and 
revealed by him to one Mandavya. 

Romaka •••Revealed by god Visnu to Rsi Romasa 
or Romaka. 

Paulisa •••Ascribed sometimes to the sage 
Pulastya, one of the seven seers or 
patriarchs forming the Great Bear 
constellation of stars (but see later). 

Surya -Revealed by the Sungod to A sura 
Maya, architect of gods, who 
propounds them to the Rsis. 

The five Siddhantas are given in the increasing 
order of their accuracy according to Varahamihira. 
Thus Varahamihira considers the Surya Siddhanta as 
the most accurate, and next in order are the Paulisa, 
and the Romaka. The Vasistha and Paitarnaha arc, 
according to Varahamihira, not accurate. 

Why were those Siddhantas regarded as *' Apauru- 
seya" (i.e. not due to any mortal man) ? Dlksit says 
{Bharatiya Jyotisdstra, Part II r Chap. 1) : 

"The knowledge of astronomy as seen developed 
during the Vedic and Vedanga Jyotisa periods and 
described in Part I, was wide as compared with the 
length of the period ; but it is very meagre, when com- 
pared with the present position***. The oldest of 
astronomical knowledge (given in the oldest Siddhantas) 
reveal a sudden rise in the standard of astronomical 
knowledge. Those who raised the standard as given 



in these works, were naturally regarded as superhuman 
and hence the available ancient works on astronomy 
are regarded as 'apawuseyd (i.e. not compiled by 
mortal men) and it is clear that the belief has been 
formed later". 

This statement, made by Dlksit nearly sixty years 
ago, really singles out only one phase of the issue, viz., 
the wide gulf in the level of astronomical knowledge of 
the Siddhantas and that in the Veddnga Jyotisa ; 
but leaves the question of actual authorship open. In 
our opinion the Siddhantas were regarded as 
Apauruseya because they appear to have been com- 
pilations by different schools of the knowledge of 
calendaric astronomy, as they diffused from the West 
during the period 100 B.C.— 400 A.D. But let us look 
into them a little more closely. 

The Paitamaha Siddhanta : described in five 
stanzas in Chap. XII. of the Paftea Siddhantika* 

As already discussed it is a revised edition of the 
Veddiiga Jyotisa ,but later authors say that it contained 
rules for the calculation of motions of the sun, the 
moon and also the planets which were not given by 
the Veddiiga Jyoli$a. As the full text of the original 
Siddhanta has not been recovered, it is difficult to say 
how the borrowal took place. 

The Vasistha Siddhanta : as known to Varahamihira 
is described in 13 couplets in Chap. II of the Pa%ca 
Siddhantika. It describes methods of calculating tithi 
and nak?aira, which are inaccurate. Besides it mentions 
liasi (zodiacal signs), angular measurements, discusses 
length of the day, and the lagna (ascendant part of the 
zodiac). Apparently this represents one attempt by a 
school to propagate western astronomical knowledge. 
The school persisted and we have Vddsiha Siddhantas 
later than Varahamihira. One of the most famous was 
Visnucandra (who was somewhat later than Aryabhata) 
who was conscious of the phenomenon of precession 
of the equinoxes. No text of the Siddhanta is 
available, except some quotations. 

Varahamihira pays a formal courtesy to Paitamaha 
and VasiMa; this does not prevent him from 
describing these two as ' duravibhrasiau\ i.e., furthest 
from truth. 

The Romaka Siddhanta : 

The Bomaka Siddhanta as reviewed by Varahamihira 
uses : 

A Yuga of 2850 years -19 x 5 x 30 years ; 
150 years = 54787 days ; 
1 year =365.2467 days. 

The number of intercalary months in the yuga is 
given as 1050, i.e., there are 7 intercalary months in 
19 years. 

We need not go any further into the contents of 
this Siddhanta. As the name indicates, the knowledge 
was borrowed from the West, which was vaguely 
known as 'Romaka* after the first century A.D. The 
yttga taken is quite un-Indian, but appears to be a 
blending of the nineteen-year cycle of Babylon, the 
five-yearly yuga of Veddiiga Jyoti§a, and the number 30 
which is the number of tithis in a month. The length 
of the year is identical with Hipparchos's (365.2467), 
and this alone of the Siddhantas gives a length of the 
year which is unmistakeably tropical. 

The Romaka Siddhanta appears to represent a 
distinct school who tried to propagate western astro- 
nomical knowledge on the lines of Hipparchos. One 
of the later propounders was Srisena, who flourished 
between Aryabhata and Brahmagupta ; the latter 
ridicules him roundly for having made a "kantha", i.e. 
a wrapper made out of discarded rags of all types — 
meaning probably Srlsena's attempt to blend two 
incongruous systems of knowledge, western and 

The Paulisa Siddhanta : 

This Siddhanta was at one time regarded as the 
rival of the Surya Siddhanta, but no text is available 
now. But it continued to be current up to the time 
of Bhattotpala (966 A.D.), who quotes from it. 

Alberuni (1030-44 A.D.) who was acquainted with 
it, said that it was an adaptation from an astronomical 
treatise of Paulus of Sainthra, i.c, of Alexandria. But 
it is not clear whether he had actually seen Paulus's 
treatise, and compared it with the Paulisa Siddhanta 
or simply made a guess on the analogy of names merely. 
The name of one Paulus is found in the Alexandrian 
list of savants (378 A.D.) but his only known work is 
one on astrology, and it has nothing in common with 
Paulisa Siddhanta, which appears to have been purely 
an astronomical treatise as we can reconstruct it from 
the PaTtca Siddhantika (vide infra). The ascription to 
Paulus of Alexandria is not therefore proved. There 
is, however, reference in the Pau'isa Siddhanta to 
Alexandria, or Yavanapura, as it was known to Hindu 
savants. The longitudes of Ujjaini and Banaras are 
given with reference to Alexandria (P. S., Chap. III). 

The Pa%ca Siddhantika devotes a few stanzas of 
Chaps. I, III, VI, VII, and VIII to this exposition of the 
Paulisa Siddhanta. Nobody seems to have gone critically 
into the contends of these chapters after Dr. Thibaut 
who tried to explain these in his introduction to the 
Paftca Siddhantika, but left most of them unexplained 
owing to their obscurity. 

In Chap. I, (verses 24—25), 30 Lords of the days of 
the month are mentioned. This is quite un-Indian 



and reminds one of the Iranian calendar in which each 
one of thirty days of the month is named after a god 
or principle (see § 2.3). The names of the lords of the 
days as given in the Paulisa Siddhanta are of course 
all Indian. 

The Surya Siddhanta 

Of all the Siddhantas mentioned by Varahamihira 
this alone has survived and is still regarded with 
veneration by Indian astrologers. This Siddhanta was 
published with annotations by Rev. E. Burgess, in 1860, 
and has been republished by the Calcutta University 
under the editorship of P. L. Gangooly, with an intro- 
duction by Prof. P. C. Sengupta. 

This is supposed to have been described by the 
Sungod to Asura Maya, the architect of the gods, who 
revealed it to the Indian Rsis. These legends certainly 
represent some sort of borrowing from the West, but 
it would be fruitless to define its exact nature unless 
the text is more critically examined. Varahamihira 
describes in Chapters IX, X, XI, XVI, XVII of the 
Paftca Siddhantika the contents of the Surya Siddhanta 
as known to him ; they are somewhat different from 
those as found in the modern text. It appears that 
this Siddhanta was constantly revised with respect to 
the astronomical constants contained in it as all 
astronomical treatises should be. The text as we 
have now was fixed up by Ranganatha in 1603 after 
which there have been no changes. Burgess, from 
a study of the astronomical constants, thought that 
the final text referred to the year 1091 A.D. Prof. 
P. C. Sengupta shows that the S.S. as reported by 
Varahamihira borrowed elements of astronomical data 
from Aryabhata, and the S.S. as current now has 
borrowed elements from Brahmagupta (628 A.D.). 

The modern Surya Siddhanta is a book of 500 
verses divided into 14 chapters, contents of which are 
described briefly below : 

Chap. I — Mean motions of the Planets. 
n II— True places of the Planets. 

Ill— Direction, Place, and Time. 
n IV — Eclipses, and especially Lunar 
V— Parallax in a Solar Eclipse. 
n VI — Projection of Eclipses. 

VII — Planetary Conjunctions. 

VIII— The Asterisms. 

IX— Heliacal Risings and Settings. 

X — Moon's Risings -and Settings, and 

the Elevation of her Cusps. 

XI — Certain malignant Aspects of the 

Sun and the Mocn-. 

Chap. XII— Cosmogony, Geography, Dimension 
of the Creation. 
„ XIII— Armillary Sphere, and other 
XIV— Different modes of reckoning Time. 

A scrutiny of the text shows that it is, with the 
exception of a few elements, almost completely astro- 
nomical. A few verses in Chap. Ill, viz., Nos. 9-12 
deal with the trepidation theory of the precession of 
equinoxes. These are regarded by all critics of the 
Surya Siddhanta to be interpolations made after the 
12th century. 

It will take us too much away from bur main theme 
to give a critical account of this treatise, but every 
critic has admitted that the text does not show any 
influence of Ptolemy's Almagest. Prof. P. C. Sen- 
gupta's introduction is particularly valuable. This 
Siddhanta indicates that longitudes should be calculated 
from Ujjain and makes no mention of Alexandria. 
Prof. Sengupta thinks that it dated from about 400 
A.D., but a scrutiny of the co-ordinates of certain stars 
marking the ecliptic, which we have discussed in 
Appendix 5-B, shows that it might have utilized data 
collected about 280 A.D., when the star Citra 
(a Virginia), was close to the autumnal equinoctial 
point, and is therefore subsequent to 280 A.D. 

The rules of framing the calendar are found in 
Chapter XII of which we give an account in the next 

After about 500 A.D., the Indian astronomers gave 
up the pretext of ascribing astronomical treatises to 
gods or mythical sages and began to claim authorship 
of the treatises they had written ; the earliest that has 
survived is that of Aryabhata (476— 523 A.D.). The 
objects of their treatises were to frame rules for 
calendaric calculations, knowledge of astronomy 
forming the basis on which these rules were 

In addition to the Surya Siddhanta only two other 
systems have survived, viz-, 

The Arya Siddhanta- due to Aryabhata II, an 
astronomer of the 10th century,_and supposed to be 
related to the Aryabhatiya of Aryabhata, who claims 
to have derived it from Brahma, the Creator. 

The Brahma Siddhanta— vaguely related to the 
Paitamaha Siddtenta, but the human authorship is 
ascribed to the celebrated astronomer Brahmagupta 
(628 A.D.). 

But a number of astronomical treatises like that of 
Siddhanta kirormni by Bhaskaracarya and many 
others, have survived either on account of their own 
merit or their connection with astrology. 



The Solar Calendar according to the 
Surya Siddhanta 

The first few verses of Chap. XII deal with the 
creation of the world according, to Hindu conception, 
and the creation of the elements ; of the sun, the 
moon, and the planets. The universe is taken to be 
geocentric, and the planets in order of their decreasing 
distances from the earth are given as (vide verse 3 J,) : 
Saturn, Jupiter, Mars, the Sun, Venus, Mercury 
and the Moon. 
The fixed stars are placed beyond the orbit of Saturn. 

Surya Siddhania> XII, Verse 32 
Mauhye samantat dandasya bhugolo byomni tisthati 
Bibhranati paramam sakfcim brahmarto dharanatmikaiii. 

Translation : Quite in the middle of the celestial 
egg (Brahmano)a\ the earth sphere (Bhugola) stands in 
the ether, bearing the supreme might of Brahma 
which has the nature of a self supporting force. 

The astronomers are thus conscious that the earth 
is a spherical body suspended in ether {byomni) 

Verse 34 : Describes the earth's polar axis, which 
passing through the earth's centre emerges as 
mountains of gold on either side. 

Verse 35 : Gods and Rsis are supposed to dwell 
on the upper (northern) pole, and the demons are 
supposed to dwell on the nether (south) pole. 

Verse 43 : Describes two pole-stars (Dhruva*taras) 
which are fixed in the sky. 

The author could have been aware only of the 
Polaris. By analogy he inferred the existence of a 
southern pole-star which, as is well-known, does 
not exist. He had apparently no knowledge of the sky 
far south of the equator. 

The remaining verses describe the equator : As in 
modern astronomy, it says that the polar star is on the 
horizon of a person on the equator and the co-latitude 
(Lambaka) of the equator is 90°. 

The Siddhantic astronomers thus completely 
accepted the geocentric theory of the solar system. It 
was a great improvement on the ideas of the world 
prevalent in India at the time of the great epic 
Mahabharata (date about 300 B.C.), in which the earth 
is described to be a flat disc, with the Sumeru 
mountain as a protruding peg in the centre, round 
which the diurnal motion of the celestial globe carrying 
the stars, planets, the sun and the moon takes place. 
This idea of the world is also found in the Jatakas and 
other Buddhist scriptures. 

In the subsequent verses four cardinal points on the 
equator are recognized, these are : 

Lanka, which is technically the name of a locality 
on the equator lying in the meridian of Ujjayini, which 
was the Greenwich of ancient India. This Lanka had 
nothing to do with Ceylon, but is a fictitious name ; 

90° west of Lanka the city called Romaka, and 
90° east of Lanka the city known as Yamakoti. 

The name Romaka vaguely refers to the capital of 
the Roman Empire. ' Yamakoti' is quite fanciful. 

The Surya Siddhanta takes it for granted that the 
sun's yearly motion through the ecliptic is known to 
the reader and now proceeds to explain the Signs of 
the Zodiac. 

Surya Siddhanta XII, 45 

Mesadau devabhagasthe devanarii yati darsanam 
Asuranam tuladau tu suryastadbhaga saficarah. 

Translation : In the half revolution beginning 
with Mesadi (lit. the initial point of Aries), the sun 
being in the hemisphere of gods, is visible to the gods, ; 
but while in that beginning with Tuladi (lit. the initial 
point of Libra) he is visible to the demons moving in 
their hemesphere. 

This means that when the sun reaches Mesadi, the 
initial point of the sign of Aries, the gods who are 
supposed to be in the north pole just witness the 
rising of the sun and has the sun over the horizon for 
six months. All these six months, the demons who are 
supposed to be at the south pole are in the dark. It 
is vice versa for their enemies the Asuras for whom, 
dwelling in the south pole, the sun rises for them 
when it is at Tuladi (beginning of the Tula sign i.e., 
first point of Libra) and remains above the horizon for 
six months. 

According to the S.S., therefore, the first point of 
Aries is coincident with the vernal equinoctial point, and 
the first point of Libra tuith the auturtinal equinoctial 

Surya Siddhanta, XIV, 9 and 10 

Bhanormakarasamkranteb sanmasa uttarayanarii 
Karkadestu tathaiva syat sanmasa daks in ay ana m. 9 , 
Dvirasinatha rtava stato'pi sisiradayat 
Mesadayo dvadasaite masastaireva vatsarah. 10, 

Translation: From the moment of the sun's entrance 
(safnkrdnti) into Makara, the sign of Capricorn, six 
months make up his northward progress (uttarayana) ; 
so likewise from the moment of entrance into Karkata, 
the sign of Cancer, six months are his southward 
progress (daksinayana). (9) 

Thence also are reckoned the seasons (rtu), the 
cool season (siUra) and the r£st, each prevailing 
through two signs. These twelve, commencing with 



Aries, are the months ; of them is made up tke 
year (10). 

These quotations leave not the slightest doubt that 
according to the compilers of the S.S., the first point 
of the zodiac is the point of intersection of the ecliptic 
and the equator, and the signs of the zodiac cover 30° 
each of the ecliptic. 

It is supposed on good grounds that much of the 
astronomical knowledge found in the Surya Siddhanta 
is derived from Graeco-Chaldean sources. But it is 
clear from the text that the compilers of the S.S. had 
no knowledge of the precession of equinoxes, but they 
took the first point of Aries to be fixed. This is not to 
be wondered at, for as shown in § 4.9, inspite of the 
works of Hipparchos and Ptolemy, precession was 
either not accepted or no importance was attached to 
it by the astronomers of the Roman empire. It may be 
added that the compilers of the S.S. were not aware 
of the theory of trepidation of equinoxes which 
appears to have been first formulated in the West by 
Theon of Alexandria (ca. 370 A.D.). It is also important 
to note that the Indian astronomers did not take the 
first point of Aries to be identical with that given 
either by Hipparchos, Ptolemy or any other western 
authority as would have been the case if there was 
blind-folded borrowing. They assimilated the astro- 
nomical knowledge intelligently and took the first 
point of Aries as the point of intersection of the 
equator and the ecliptic, and made successive attempts 
to determine it by some kind of actual observations, 
as shown in appendix 5-B. These observations appear 
first to have been made about 280 A.D. 

Length of the Year 

The length of the year, according to the different 
authorities are as follows, 

Surya Siddhanta of days 

Varahamihira ... 365 d 6 U 12- 36" =365.25875 

Current S.S. ... 365 6 12 36.56 = 365.258756 

Ptolemy (sidereal) 365 6 9 48.6 = 365.256813 
Correct length of 

the sidereal year. .. 365 6 9 9.7 = 365.256362 
Correct length of 

the tropical year- 365 5 48 45.7 = 365.242196 

N. B. Varahamihira's length of the year is also found in 
Aryabhata's ardhardtrika, or midnight system, and in 
Brahmagupta's Khari^ix Khadyaka. 

How did the. Indian savants manage to have such a 
wrong value for the length of the year ? 

The year, according to the Surya Siddh&nta, is 
meant to be clearly tropical, but as the Indian savants 
compiling the S.S. were ignorant of the phenomenon of 

precession of the equinoxes, they were unaware of the 
distinction^ between the sidereal year and the tropical 
year. They had to obtain the year-length either from 
observation or from outside sources. If they obtained 
it from observations, they must have counted the 
number of days passed between the return of the sun 
to the same point in the sky over a number of years. 
Such observations would show that the year had not 
the traditional value of 366 days given in Vedanga 
Jyotisa, but somewhat less. In fact, the Paitamaha 
length is 365.3569 days and there is no reason to 
believe that it was derived from foreign sources. 
Successive observations must have enabled the Indian 
savants to push the accuracy still higher. 

Or alternatively they might have borrowed the 
value from Graeco-Chaldean astronomy, but we cannot 
then explain why their value is larger than Ptolemy's. 
We have seen that the Romaka Siddhanta gives a value 
which is Hipparchos's, and tropical, but the three more 
correct SiddhSntas reject it, as being too small. This 
however indicates that they probably tried to derive 
the length from observations as stated in the previous 
paragraph and found the Romaka SiddhantaAength. too 
small. If they had taken it from some other source, 
we have still to discover that source. It is certainly 
not Ptolemy's Almagest 

The ex-cathedra style of writing adopted by the 
Siddhantic astronomers, e.g., the number of days in a 
Kalpa (a period of 4.32 x 10* years) is 1,577,917,828,000 
according to Grandfather Brahma, or the Sungod, 
does not enable one to trace the steps by which these 
conclusions were reached. 

The two problems of (i) distinguishing between the 
tropical year, and the sidereal year and of (ii) deter- 
mining the correct length of the year in terms of 
the mean solar days are very exacting ones. 

We have seen how it took the West the whole 
time-period between 3000 B.C. to 1582 A.D. to arrive 
at the idea that the true length of the tropical year 
was close to 365.2425 days. Probably Iranian astrono- 
mers of Omar Khayam's time (1072 A.D.), who had the 
advantage of the great Arabian observations by al- 
Battanl and others had a more correct knowledge of 
this length. The final acceptance of the distinction 
between the tropical and the sidereal year dates only 
from 1687 A.D., when Newton proved the theory of 
trepidation to be wrong. 

The Siddhantic astronomers of 500-900 A.D. cannot 
therefore be blamed for their failure to grasp the two 
problems. But what to say of their blind followers 
who, in the twentieth century, would continue to 
proclaim their belief in the theory of trepidation ? 



Effect of continuance of the mistake 

The Surya Siddh&nta value, vix. t 365.258756 days is 
larger than the correct sidereal value by "002394 days 
and larger than the tropical length by .016560 days. 

As the S.S. value is still used in almanac-framing, 
the effect has been that the year-beginning is advancing 
>y .01656 days per year, so that in course of nearly 1400 
years, the year-beginning has advanced by 23.2 days, 
so that the Indian solar year, instead of starting on the 
day after the vernal equinox (March 22) now starts on 
April 13th or 14th. The situation is the same as 
happened in Europe, where owing to the use of a 
year-length of 365.25 days, since the time of Julius 
Caesar, the Christmas preceded the winter solstice by 
10 days, when the error was rectified by a Bull of 
Gregory XIII, and the calendar was stabilized by 
introducing revised leap-year rules. 

The Calendar Reform Committee has proposed that 
the Indian New Year should start on the day after the 
vernal equinox day. Most of the Indian calendar 
makers belong to the no-changer school, or the 
nirayana school (i.e., school not believing in the 
precession of the equinoxes). But this school does 
not realize that even if the sidereal length of the year 
be acceped, the Indian year-length used by them is 
larger by nearly '0024 days, which cannot be tolerated. 
So if a change has to be made, it is better to do it 
whole -hog, i.e., take the year-length to be tropical, and 
start the year on the day after the vernal equinox. 

This is the proposal of the Indian Calendar Reform 
Committee, and it is in full agreement with the canons 
laid down in the Surya Siddhanta. 

Historical Note on the Year-beginning 

The Indian year, throughout ages, has been of two 
kinds, the solar and the lunar, each having its own 
starting day- The year-beginning for the two kinds 
of years, for different eras* is shown in Table No. 27. 

The Starting Day of the Solar Year 

In the Vedic age, the year-beginning was related 
probably to one of the cardinal days of the year, but 
we do not know which cardinal day it was. The 
Ved&iiga Jyotisa started the year from the winter 
solstice day, Brdhmaws started the year from the 
Indian Spring (Vasanta) when the tropical (Say ana) 
longitude of the sun amounted to 330°. 

The Siddhantic astronomers must have found a 
confusion, and so fixed up a rule for fixing the year- 
beginning, which we have just now dicussed. These 
rules amount to : 

(a) Starting the astronomical year from the 
moment the sun crosses the vernal equinoctial point. 

(b) Starting the civil year on the day following. 

The Siddhantic astronomers thus brought the 
Indian calendar on a line with the Graeco-Chaldean 
calendar prevalent in the Near East during the 
Seleucid times. 

In a few cases, e.g., in the case of the Vikrama 
era reckoning as followed in parts of Guzrat, the year- 
beginning is in Kartika. This seems to be reminiscent 
of the custom amongst the Macedonian Greek rulers 
of Babylon to* start the year on the autumnal equinox 

The First Month of the Year : 

This has to be defined with respect to the defini- 
tion of the seasons. 

According to modern convention, which is derived 
from Graeco-Chaldean sources, the first season of the 
year is spring ; it begins on the day of vernal equinox, 
as shown in fig. 25 which shows also the other seasons. 
The Indian classification of seasons is, however, 
different as the following table shows. 

Table 15 — Indian Seasons. 

— 30° to 30°... Spring (Vasanta) Caitra & Vaisakha 
30 to 90 . . .Summer (Grisma) Jyaistha & A^iidha 
90 to 150 ...Rains (Varsa) ^ Sravana & Bhadra 
150 to 210 ...Early Autumn (Sarat) Asvina & Kartika 
210 to 270 ...Late Autumn Agrahayana & Pausa 


270 to 330 ...Winter (Sisira) Magna & Phalguna 

The Siddhantic astronomers, therefore, found 
themselves in a difficulty. If they were to follow 'the 
Indian convention, Caitra would be the first month 
of the solar year. If they were to follow tfie Graeco- 
Chaldean covention, they had to take VaUakha as 
the first month of the solar year. 

They struck a compromise. For defining the solar 
year, they took Vaisakha as the first month and for 
defining the lunar year they took Caitra as the first 
month (see § 5*7). 

But this rule has been followed only in North 
India. In South India, they had different practices, 
as shown in the list of solar month -names (Table 
No. 16). 

In North India the first month is Vaisakha as 
laid down in the S.S. which starts just after sun's 
passage through the V.E. point. 

It is interesting to see that in Tamil Nad, some of 
the names are of Sanskritic origin, others are of Tamil 
origin. But the most striking fact is that the first mouth, 
starting after vernal equinox is not Vaisakha as in the 



Table 16. 

Indian Names 
of Signs 

Corresponding Names of Solar Months. 




or S. Malayalam 

N. Malayalam 













A s^dha 


























Arppisi (Aippasi) 

































(The first month of the year has been distinguished by capitals). 

taken without change from Sanskrit. The Assamese 

N.B. The Bengali or Oriya names of solar months are 
names are the same, but have local pronunciations. 

rest of India but Ghittirai or Caitra, and so on. We do 
not know why Tamil astronomers adopted a different 
convention. We can onlv guess : probably they wanted 
to continue the old Indian usage that Caitra is to 
remain the first month of the year. 

In Tinnevelley and Malayalam districts the solar 
months are named after the signs of the zodiac. 

There is, therefore, no uniformity of practice in the 
nomenclature of the solar months, and in fixing up 
the name of the first month of the solar year. 

Solar Months : Definition 

After having defined the solar year, and the year 
beginning, the Surya Siddhanta proceeds to define the 
"Solar Month." 

Surya Siddhanta, Chap. 1,13 

Aindavastithibhi-stadvat samkrantya saura ucyate 
Masairdvadasabhirvarsarii divyam tadaharucyate. 

Translation : A lunar month, of as many lunar 
days, (fithi) ; a solar (saura) month is det2rmined by 
the entrance of the sun into a sign of the zodiac, i.e. 
the length of the month is the time taken by the sun 
in passing 30° of its orbit, beginning from the 
initial point of a sign ; twelve months make a year, 
this is called a day of the gods. 

This definiton is accepted by the Arya, and 
Brahma Siddhantas as well. 

The working of this rule gives rise to plenty of 
difficulties, which are described below : 

The mean length of a solar month 

-30.43823 according to S.S. 

=* 30.43685 according to modern data. 

The actual lengths of the different solar months* 
however, differ widely from the above mean values. 
This is due to the fact that the earth does not move 
with uniform motion in a circular orbit round the sun, 
but moves in an elliptic orbit, one focus of which is 
occupied by the sun, and according to Kepler's second 
law, it sweeps over equal areas round the sun in equal 
intervals of time. When the earth is farthest from 
the sun, i.e. at aphelion (sun at apogee) of the 
elliptic orbit, the actual velocity of the earth becomes 
slowest, and the apparent angular velocity of the 
sun becomes minimum, and consequently the length 
of the solar month is greatest. This happens about 
3rd or 4th July, i.e., about the middle of the solar 
month of Asadha (Mithuna), and consequently this 
month has got the greatest length. The circumsfances 
become reversed six months later on about 2nd or 3rd 
January, when the earth is nearest to the sun, i.e., at 
perihelion (sun at perigee), the angular velocity of the 
sun at that time becomes maximum, and consequently 
the solar month of Pausa (Dhanufy) which is 
opposite to Ssadha, has got the minimum length. 
The following two figures ( Nos. 25 & 26 ) will explain 
the position. 

The durations of the different months, which are 
different from each other due to the above reason, are 
also not fixed for all time. The durations of the solar 



months undergo gradual variations on account of two 
reasons ; v%%.$ 


Fig. 25 

(i) the line of apsides of the earth's elliptic orbit 
the aphelion and perihelion points) is not fixed 

Fig. 26 

in space but is advancing along the ecliptic at the 
rate of 61".89 per year or l.°72 per century. This is 

Table 17 — Lengths of different solar 

made up of the precessional velocity of 50. "27 per year 
in the retrograde direction and the perihelion velocity 
of 11. "62 per year in the direct direction due to 
planetary attraction. This movement of the apse line 
with respect to the V.E. point causes variation in the 
lengths of the different months. 

(ii) The second reason is that the ellipticity 
of the earth's orbit is not constant ; it is gradually 
changing. At present the eccentricity of the orbit is 
diminishing and the elliptic orbit is tending to become 
circular. As a result, the greatest duration of the 
month is diminishing in length and the least one 
increasing. Similarly the lengths of other months are 
also undergoing variation. 

The modern elliptic theory of planetary orbits was 
not known to the makers of Indian Siddhantas, but 
they knew that the sun's true motion was far 
from uniform. They conceived that the sun has 
uniform motion in a circle, with the earth not 
exactly at the centre of that circle, but at a 
small distance from it. The orbit therefore becomes- 
an eccentric circle or an epicycle. Here also the 
angular motion of the sun becomes minimum when at 
apogee or farthest from the earth, and maximum when 
nearest to the eartn or at perigee. In this case the 
size and eccentricity of the circle are invariable 
quantities, and consequently the maximum and 
minimum limits of the months are constant. The 
apse line advances in this case also, but with a very 
slow motion, which according to the Surya Siddhanta 
amounts to a degree of arc in 31,008 years, or 11" in a 
century. The variations of the durations of months 
due to this slow motion of the apse line is quite 
negligible and the lengths of the months according to 
the Surya Siddhanta are practically constant over ages. 

months reckoned from the vernal equinox. 

Lengths of Solar months. 

According to 

Modern value 

SUrya Siddhanta 

(1950 A.DJ 

{as proposed) 












Vaisakha (Me$a) 

( o c 

J -30° ) 








Jyais^ha (Vftfa) 

( 30 

-60 ) 








A$adha (Mithuna) 

( 60 

-90 ) 








t^ravana (Karka^a) 

( 90 

-120 ) 







A sad ha 

Bhadra (Simha) 


-150 ) 







Asvina (Kanya) 


-180 ) 








Kartika (Tula) 


-210 ) 








Agrahayana (Vrscika) 


-240 ) 








Pausa (Dh&nub) 


-270 ) 








Magna (Makara) 


-300 ) 








Phalguna (Kumbha) 


-330 ) 








Caitra (Mina) 


-360 ) 














O.B.— 39 



In the Surya Siddhdnta, a formula is given for 
finding the true longitude of the sun from its mean 
longitude. As the length of a month is the time taken 
by the sun to traverse arcs of 30° each along the 
ecliptic by its true motion, the lengths of the different 
months can be worked out when its true longitudes on 
different dates of the year are known. The true 
longitude is obtained by the Surya Siddhdnta with the 
help of the following formula : 

True Long. — Mean Long. — 133. '68 sin K 

+ 3.18 sin 2 K 

where K~ Mandakendra of the sun, 
i.e., — mean sun — sun's apogee. 

Different conventions for fixing up the 
beginning of the solar month 

The safnkranti or ingress of the sun into the 
different signs may take place at any hour of the day. 
Astronomically speaking the month starts from that 
moment. But for civil purposes, the month should 
start from a sunrise ; it should therefore start either 
on the day of the safnkranti or the next following 
day according to the convention adopted for the 
locality. There are four different conventions in 
different States of India for determining the beginning 
of the civil month. 

At the approximate time of each safnkranti, the 
true longitude of the sun is calculated by the above 
formula for two successive days, one before the 
attainment of the desired multiple of 30° of longitude 
and the other after it, and then the actual time of 
crossing the exact multiple of 30th degree is obtained 
by the rule of simple proportion. This is called the 
time of safnkranti or solar transit. The time interval 
between the two successive safnkrdntis is the actual 
length of the month, The lengths of the months thus 
derived from the Surya Siddhdnta compared with the 
modern values, i.e., the values which we get after 
taking the elliptic motion of the sun, and the shift of 
the first point of Aries are shown in Table No. 17, 
on p. 243, in which : — 

Column (1) gives the names of months. 

„ (2) gives the arc measured from the first 

point of Aries (the V.E. point) 
covered by the true longitude 
of the sun. 

„ (3) gives the lengths of the months 

derived from the Surya- 
Siddhdnta rules. 

(4) gives the correct lengths of the 

months as in 1950 A.D. 

(5) gives the corresponding names of the 

months as proposed by the 

It would appear from table No. 17 that the 
lengths of the months of the Surya Siddhdnta are no 
longer correct ; they greatly differ from their corres- 
ponding modern values, sometimes by as much as 11 J 
hours. The Surya Siddhdnta value s, which the 
almanac makers still use, are therefore grossly 
incorrect. Moreover, the lengths of the months are 
undergoing gradual variation with times due to reasons 
already explained. 

Rules of Samkranti 

The Bengal rule : In Bengal, when a safnkranti 
takes place between sunrise and midnight of a civil 
day, the solar month begins on the following day ; and 
when it occurs after midnight, the month begins on 
the next following day, i.e., on the third day. This is 
the general rule j but if the safnkranti occurs in the 
period between 24 minutes before midnight to 24 
minutes after midnight, then the duration of tithi 
current at sunrise will have to be examined. If the 
tithi at sunrise extends up to the moment of safnkranti, 
the month begins on the next day : if the tithi ends 
before safnkranti, the month begins on the next 
following or the third day. But in case of Karkata 
and Makara safnkrdntis, the criterion of tithi is not 
to be considered. If the Karkata safnkranti falls in 
the above period of 48 minutes about the midnight, the 
month begins on the next day, and if the Makara 
safnkranti falls in that period, the month begins on the 
third day. 

The Orissa rule : In Orissa the solar months of the 
Amli and Vilayati eras begin civilly on the same day 
(sunrise to next sunrise) as the safnkranti, irrespective 
of whether this takes place before or after midnight. 

The Tamil rule : In the Tamil districts the rule is 
that when a safnkranti takes place before sunset, the 
month begins on the same day, while if it takes place 
after sunset the month begins on the following day. 

The Malabar rule : The rule observed in the North 
and South Malayalam country is that, if the samkranti 
takes place between sunrise and 18 ghatykds (7 h 12 U1 ) 
or more correctly fth of the duration of day from 
sunrise (about 1-12^ P.M.) the month begins on the 
same day, otherwise it begins on the following day. 

It will be observed that as a result of the different 
conventions combined with the incorrect month- 
lengths of the Surya Siddhdnta we are faced with the 
following problems 



(1) the civil day of the solar month-beginning 
may differ by 1 to 2 days in different parts of India. 

(2) The integral number of days of the different 
solar months also vary from 29 to 32. 

The months of Kartika, Agrahayatya, Pau§a, Magha 
and Phalguna contain 29 or 30 days each, of which 
two months must be of 29 days, and others of 30 days. 
The months Caitra, Vai&akha and Asvina contain 30 
or 31 days. 

The • rest, vix., Jyaistha, Asa4ha, Sravana and 
Bhadra have got 31 to 32 days each, of which one or 
two months will contain 32 days every year. 

(3) The length of the month by integral number 
of civil days is not fixed, it varies from year to year. 

Justification of the Solar Calendar as proposed 
by the Committee 

It has been shown that the intention of the maker 
of Surya Siddhanla and of other Siddhantas was to 
start the year from the moment of sun's crossing the 
vernal equinoctial point and to start the civil year 
from the day following. The Committee has also 
adopted this view and proposed that the civil year 
for all-India use should start from the day following 
the V. E. day, i.e., from March 22. In the Vedic 
literature also it is found that the starting of the year 
was related with one or other of the cardinal days of 
the year. The Vedafiga Jyotisa started the year from 
the winter solstice day, the Brahmanas started the 
year from the Indian spring (Vasanta) when the 
tropical {Sayana) longitude of the sun amounted to 
330°, but in the Siddhantic period the year-beginning 
coincided with the V.rE. day. So in adopting the 
Sayana system in our calendar calculations, the 
Indian tradition, from the Vedic times up to the 
Siddhantic times, has been very faithfully observed. 
This has ensured that the Indian seasons would 
occupy permanent places in the calendar. 

As regards the number of days per month, although 
the Surya Siddhanta defines only the astronomical 
solar month as the time taken by the sun to traverse 
30° of arc of the ecliptic, four different conventions 
have been evolved in different States of India for 
determining the first day of the civil month from the 
actual time of transit as narrated earlier. None of 
the conventions is perfect. Such rules do not yield 
fixed number of days for a month, as a result of 
which it becomes extremely difficult for a chrono- 
logist to locate any given date of this calendar, 
unambiguously, in the Gregorian calendar, without 
going through lengthy and laborious calculations. 
Moreover, the number of days of months obtained 

from such rules vary from 29 to 32, which is very 
inconvenient from various aspects of civil life. 

The Committee has therefore felt that there is no 
need for keeping the solar months as astronomically 
defined. The length of 30 and 31 days are quite 
enough for civil purposes. Moreover, fixed durations 
of months by integral number of days is the most 
convenient system in calendar making. The five 
months from the second to the sixth have the lengths 
of over 30| days, and so their lengths have been 
rounded to 31 days each ; and to the remaining 
months 30 days have been allotted. 


The broad divisions of the year into seasons or 
months are obtained by the solar calendar, but since 
for religious and social puposes the lunar calendar had 
been used in India from the Vedic times, it becomes 
incumbent to devise methods for pegging on the lunar 
calendar to the solar. 

The extent to which the lunar calendar affects 
Indian socio-religious life will be apparent from the 
tables of holidays we have given on pp. 117-154. There 
the religious and social ceremonies and observances 
and holidays of all states and communities are classified 
under the headings : 

(1) Regulated by the solar calendar of the 
Siddhantas ; 

(2) Regulated by Gregorian dates ; 

(3) Regulated by the lunar calendar. 

The tables show that by far the largest number of 
religious holidays and other important social ceremonies 
are regulated by the lunar calendar. It is difficult to 
see how the lunar affiliation, inconvenient as it is, can 
be replaced altogether, short of a revolution in which 
we break entirely with our past. The -lunar calendar 
will therefore continue to play a very important part 
as we continue to keep Our connection with the past, 
and with our cherished traditions. 

Let us now restate the problems which arise when, 
with reference to India, we want to peg the lunar 
calendar to the solar, how it was tackled in the past, 
and how the Calendar Reform Committee wants to 
tackle it. 

The lunar month consists of 29.5306 days and 12 
such lunar months fall short of the solar year by 10.88 
days. After about 2 or 3 years one additional or inter- 
calary lunar month is therefore necessary to make up 
the year ; and in 19 years there are 7 such intercalary 
months. In Babylon and Greece there were fixed rules 



for intercalation ; the intercalary months appeared at 
stated intervals and were placed at fixed positions in 
the calendar (vide § 3.2). It appears that some kind of 
rough rules of intercalation of lunar months were 
followed in India up to the first or second century 
A.D. when the calendar was framed according to 
the rules of Vedaiiga Jyoti§a (vide § 5.4). Thereafter 
the Siddhantic system of calendar-making began 
to develop, replacing the old Vedaiiga calendar. 

The Vedaiiga calendar as we have seen was crude 
and was based on approximate values of the lunar and 
solar periods, the calendar was framed on the mean 
motions of the luminaries, and as such an intercalary 
month was inserted regularly after every period of 
30 months. 

The Siddhanta Jyotisa introduced the idea of true 
positions of the luminaries as distinct from their mean 
positions, and devised rules for framing the calendar 
on the basis of the true positions, and adopted more 
correct values for the periods of the moon and the 
sun. But some time elapsed before new rules were 
adopted, and intercalary months continued to be 
calculated on the basis of the mean motions of the 
sun and the moon, employing however more correct 
values of their periods as given by the Siddhantas. In 
this connection the following remarks by Sewell and 
Dlksit, in the Indian Calendar (p. 27) are worth noting. 

"It must be noted with regard to the intercalation and 
suppression of months, that whereas at present these are 
regulated by the sun's and moon's apparent motion, — in other 
words, by the apparent length of the solar and lunar months 
— and though this practice has been in use at least from 
1100 A.D. and was followed by Bhaskaracaryn, there is 
evidence to show that in earlier times they were regulated 
by the mean length of months. It was at the time of the 
celebrated astronomer Sripati (1039 A.D.) that the change 
of practice took place". 

Intercalary months or Malamasas. 

The length of the Surya Siddhanta year is 365.258756 
days and of a lunar month according to the S. S. is 
29.5305879 days. Twelve such lunar months fall short 
of the S. S. year by 10.891701 days. The lunar year 
therefore slides back on the solar scale each year by 
about 11 days. If the months were allowed to slide 
back continuously it would have completed the cycle 
in 33.5355 years, and the festivals attached to the lunar 
calendar would have moved through all the seasons 
of the year within this period, as now happens with the 
Islamic calendar. 

To prevent the occurrence of this undesirable 
feature, the system of intercalary months or mala m&sas 

have been introduced. Taking the mean vaules of the 
lunation-period and of the length of the solar year, 
the time when one extra month (i.e., intercalary month) 
will have to be introduced can easily be determined. 
But the luminaries do not move with uniform angular 
motions [throughout their period of revolution and so 
the determination af the intercalary month on the 
basis of the actual movement of the sun and the moon 
is a very difficult problem. The calculations according 
to the mean motions are however shown below. 

Table 18 — Calculation of intercalary months in a 

19-year cycle. 



Length of year 365.258756 
Solar month 30.438230 
Lunation 29.53Q581 
No. of solar months 

after which a lunar 

month is added 32.5355 

19 years = 
235 lunations 
( = 19x12 + 7) 

Error in the 
19-year cycle 







- 0.18078 



29 530588 


+ 0.08617 

It would appear from the above figures that the 
19-year cycle with 7 mala masas is a better approxi- 
mation if we adopt the tropical year, and the error 
gradually increases with the sidereal year and the 
Surya Siddhanta year. In Hi cycles, i.e., in 220 years, 
the discrepancy would amount to only a day in the 
case of the tropical year. 

It is also seen that one intercalary month is to be 
added at intervals of 32* solar months, or in other 
words an intercalary month recurs alternately after 32 
and 33 solar months. According to this scheme the 
intercalary months in a period of 19 years would be as 
follows : — 



Intercalary month 
9 Margaslrsa 
5 SrSvana 
2 Vaisakha 

Year Intercalary month 

11 10 Pausa 

12 — 

13 — 

14 7 Ssvina 

15 ~ 

16 — 

17 3 Jyestha 

18 — 

19 12 Phal^^a 



But the makers of Indian calendars have not 
followed any scheme for intercalation based on mean 
motions. They evolved a plan for distinguishing an 
intercalary month from a normal month based on the 
true motions of the sun and the moon. This plan is 
also followed in giving the name to a lunar month, as 
explained below : 

Siddhantic rules for the Lunar Calendar 

There are two kinds of lunar months used in India, 
the new-moon ending and the full-moon ending. In 
calendarical calculations only the new-moon ending 
months are used. 

(i) The new-moon ending lunar month covers the 
period from one new-moon to the next. This is known 
as amanta or mukhya candra mdsa. It gets the same 
name as the solar month in which the moment of initial 
new-moon of the month falls. For this purpose the 
solar month is to be reckoned from the exact moment 
of one safnkranti of the sun to the moment of the next 
safnkranti. When a solar month completely covers 
a lunar month, i.e., when there are two moments of 
new-moon (amanta), one at the beginning and the other 
at the end of a solar month, then the lunar month 
beginning from the first new-moon is the intercalary 
month, which is then called an adhika or mala masa, 
and the lunar month beginning from the second new- 
moon is the normal month which is termed as suddha 
or nija in the Siddhantic system. Both the months 
bear the name of the same solar month but are prefixed 
by adhika or suddha as the case may be. In an adhika 
month religious observances are not generally allowed. 

If on the other hand, a lunar month completely 
covers a solar month, no new-moon having occurred 
in that solar month, the particular lunar month is then 
called a ksaya or decayed month. 

As the mukhya or new-moon ending lunar month 
begins from the Amavasyd or the new-moon occurring 
in the solar month bearing the same name, the lunar 
month may begin on any day during that solar month 
— it may begin on the first or even on the last day of 
that solar month. 

(ii) The full-moon ending lunar month known as 
purnirnanta or gauna candra masa, covers the period 
from one full-moon to the next, and is determined on 
the basis of the corresponding new-moon ending month 
as defined above. It begins from the moment of full- 
moon just a fort-night before the initial new-moon of 
an amanta month, and it also takes the name of that 

But in the gaunamdna (i.e., full-moon ending lunar 
month), as the month starts 15 . days earlier than the 

new-moon ending month, it may begin on any day 
during the last half of the preceding solar month and 
the first half of the solar month in question. It will 
therefore be seen that while the new*moon ending or 
mukhya month sometimes falls almost entirely out- 
side (i.e, % after) the relative solar month, the full-moon 
ending or a gauna month always covers at least half of 
the solar month' of that name. 

The months used for civil purposes in the Hindi 
calendar are the full-moon ending lunar months, and 
are sub-divided into two halves — kf$na pak$a covering 
the period from full-moon to new-moon and termed 
as vadi, and sukla paksa covering the period from new- 
moon to full-moon and termed as sudi. As these 
months are on the gaum mana, the vadi half of a 
month comes first followed by the sudi half. The last 
day of the year is therefore a full-moon day, the 
Phalgunl (or Holi ) Purnima, in keeping with the 
ancient Indian custom. 

The Samvat and Saka years in the Hindi calendar 
begins with Caitra Sukla Pratipad. For astronomical 
purposes, however, the year begins a few days later 
with the entrance of the sun into Mesa. 

The calendars of Asaq^hi Safnvat and Karlikl Safnvat 
are, on the other hand, based on the new-moon ending 
months, and consequently the months begin 15 days 
later than the months of the Caitradi full-moon ending 
calendar. The A sa^hl calendar begins with Asa4ha 
Sukla 1, and the Kartikl calendar with Kartika 
Sukla 1. 

The table (No. 20 on p. 249) shows the scheme of 
the different calendars for the year ^aka 1875 
(1953-54). The year contains a mala or adhika month. 

It may be seen from the above mentioned table 
that in case of the light half of the month (sudi half) 
the month has the same name for the two systems of 
month-reckoningsi but in the dark half of the month 
(vadi half) the names of the months in the two systems 
are different. 

The year-beginnings of the Samvat era in the three 
systems of luni -solar calendar are also different, as may 
be seen from the following table. 

Table 19 — Showing the year-beginnings of the 
different systems of Samvat era. 

Calendar Caitradi 

Safnvat era 2010 






of year Caitra S 1 Asadha S 1 Kartika S 1 
(16 Mar., 1953) (12 July, 1953) (7 Nov., 1953) 



Counting of the Succession of Days 

In all the calendars used in India, days are counted 
according to the solar reckoning, as well as according 
to the lunar reckoning {i.e., by tithi or lunar day). 
But there is a difference in emphasis. 

In the eastern regions (Bengal, Orissa and Assam), 
and in Tamil Nad and Malabar, the solar reckoning is 
given more prominence. The almanacs give solar 
months and count the days serially from 1 to 29, 30, 
31 or 32 as the case may be. The tithi endings are 
given for every day, and the tithi may start at any 
moment of the day. 

In other parts of India (except Bengal, Orissa, 
Assam and Tamil Nad), the counting of days is based 
on the lunar reckoning, and the number of the tithi 
current at sunrise is used as the ordinal number of 
the date necessary in civil affairs. So there are 29 or 
30 days in a month, but the days are not always 
counted serially from 1 to 29 or 30. 

The month in the lunar calendar is divided into 
two half-months, the sudi and vadi halves in the new- 
moon ending system, and the vadi and kudi halves in 
the full-moon ending system. In fact the year is 
divided into 24 half-months instead of 12 months. So 
there are 14 to 15 days in a half-month {vide Table 20). 

The tithi or lunar day is measured by the positions 
of the moon and the sun. When they are in conjunc- 
tion, i.e., at new-moon the 30th tithi or amavasya ends 
and the first tithi starts which continues upto the 
moment when the moon gains on the sun by 12° in 
longitude. Similarly when the difference between the 
moon and the sun is 24° the second tithi ends, and so 
on. The average duration of a tithi is 23 h 37 . m 5, but 
the actual duration of a particular tithi undergoes 
wide variations from the above average according to 
the different positions of the sun, the moon and the 
lines of their apsides. It may become as great as 
26 h 47 m and as small as 19 b 59 m . So generally to every 
day there is a tithi. But sometimes a tithi begins and 
ends on the same civil day, and such a tithi is dropped ; 
and some religious ceremonies of auspicious character 
are not allowed to take place on such a tithi, and the 
following day begins with the next following tithi. 
For example, if the third tithi is dropped, the sequence 
of days of the half-month is 1, 2, 4, 5 etc., thus the 
seriality is broken here. 

As opposed to the above-mentioned case, the tithi 
sometimes extends over two days, there being no tithi 
ending in a day (from sunrise to next sunrise). As the 
same tithi remains current on two successive sunrises, 
the same tithi-numbex is allotted to both the days j 
in the second day, however, it is suffixed by the term 

'adhiha*. For example if the third tithi is repeated, 
then the sequence of days of the half-month would be 
1, 2, 3, 3 adhiha, 4, etc. 

Some improvement in the use of tithi for dating 
purposes is, however, observed in the Fusli calendar 
in vogue in some parts of Northern India. In this 
calendar the month begins from the day following the 
full- moon and dates are counted consecutively 
from 1 to 29 or 30 without any break at new-moon, or 
any gapping or over-lapping of dates with k$aya tithi 
or adhiha tithi. In fact the dates of 'this calendar 
have no connection with iithis after the starting of 
the month has been determined. The year of Fusli 
begins after the full-moon day of lunar Bhadra 

Mala Masa and Kshaya Masa 

It has been stated before that even at the beginning 
of the Siddhanta Jyotisa period, the intercalary months 
{mala or adhiha) were determined on the basis of the 
mean motions of the sun and the moon, and as such 
there was no possibility of the occurrence of any so 
called ksaya or decayed month. But as already 
mentioned, from about 1100 A.D., the intercalary 
months are being determined on the basis of the 
true motions of the luminaries, i,e., on the actual 
lengths of the new-moon-ending lunar month and 
of the different solar months as obtained from 
Siddhantic rules. This gave rise to the occurrence 
of ksaya months, and the intercalary months 
were also placed at very irregular intervals. 

The period from new-moon to new-moon (the lunar 
month ) is not a period of fixed duration ; it varies 
within certain limits according to the different 
positions of the apse line of the lunar and solar orbits, 
as follows : — 

Length of the Lunation 

By mean motion According to S.S. Modern 

a li d h d h 

29 6.3 29 5.9 
29 12.73 to to 

29 19.1 29 19.6 

Comparing these values with the actual lengths of 
solar months given in Table 24, it is observed that the 
minimum length of the lunar month falls short of all 
the solar months, even of the shortest month of Pawa. 
But as a mala masa is not possible in that month, the 
maximum and minimum limits of the lunar months are 
recalculated for each of the solar months from 
Kartika to Fhalguna separately. 

Table 20. 

Scheme of the Lani-Solar Calendar 

( Saka 1875 = 1953-54 A.D. ) 


Religious Calendar 

Civil Luni-Solar Calendar 

Mukkya or new- 
moon ending 

Caitra S 

Caitra K 

Vai&akha S 

Vamkha K 

Vaisakha S 

Vaisakha K 

Jyestha S 

Jyestha K 

Asadha S 

Asadha K 

Sravana S 









Phalguna S 
Phalguna K 


Gauna or full- 
moon ending 

Caitra S 

Vaisakha K 

Vai&ahha S 

Vaisakha K 

Vaisakha S 

Jyestha K 



travail a E 
Sravana S 
Phalguna K 
Phalguna S 
Caitra K 



Caitra S 

Vaisakha V 

Vaiixkha S 

Vaisakha V 

Vaisakha 3 
Jyestha V 















Phalguna S 
Caitra V 














Caitra S 
Caitra V 
Vamkha S 

Vaiiakha V 

Vaisakha S 
Vaisakha V 

Jyestha S 
Jyestha V 
Asadha S 
Phalguna S 
Phalguna V 














Initial date reckoned on the 
Solar Calendar as is now 
in use. 

Indian Solar 
Calendar date 

2 Caitra 
17 Caitra 
1 Vaisakha 

17 Vaisakha 

31 Vaisakha 
15 Jyestha 

29 Jyestha 
14 Asadha 
28 Asadha 
11 Sravana 
25 Sravana 
9 Bhadra 
24 Bhadra 
8 Asvina 
23 Asvina 
6 Kartika 
21 Kartika 

5 Agrah. 

21 Agrah. 

6 Pausa 

22 Pausa 
6 Magha 

21 Magha 

6 Phalguna 

22 Phalguna 
6 Caitra 

Gregorian date 

16 Mar. 
31 Mar. 
14 Apr. 

30 Apr. 

14 May 
29 May 

12 June 

28 June 

12 July 

27 July 

10 Aug. 

25 Aug. 
9 Sep. 

24 Sep. 

9 Oct. 

23 Oct. 

7 Nov. 

21 Nov. 

7 Dec. 
21 Dec. 

6 Jan, 1954 
20 Jan. 

4 Feb. 
18 Feb. 

6 Mar. 
20 Mar. 

S — $ukla paksa or 
K = Krsna paksa. 


When the lunar month 
nearly covers the 
Solar month of 

Kartika or Phalguna 
Agrahayana or Magha 

V= . 

Length of the lunar month. 
Minimum Maximum 

29 9.7 
29 10.5 
29 10.8 

29 18.0 
29 18.8 
29 19.1 

or Vadi. 

Comparing the above limits with the actual lengths 
of months stated before, it is found that the minimum 
length of the lunar month falls short of all the solar 
months except Pausa. So a malamdsa or intercalary 
month is possible in all the months except * the month 
of ibtisd only. 



The maximum duration of a lunar month, on the 
other hand, exceeds the lengths of the solar months 
only in case of solar Agrahdyana, Pausa and Magha. So 
a ksaya month is possible only in these three months. 

A list is given below showing the actual intercalary 
months occurring during the period Saka 1823 (1901-2 
A. D. ) to Saka 1918 (1996-97 A. D. ) on the basis of 
Surya Siddhanta calculations. 

Table 21. 

Intercalary months in the present century 


























Asvina, Caitra 
















































Pausa is Ksaya, 

* + Magha is Ksaya. 

As regards the ksaya months that occurred and 
will be occurring during the period from 421 Saka 
(49S-500 A D.) to 1885 iSaka (1963"64 A.D.) a statement 
is given below showing all such years mentioning the 
month which is ksaya and also the months which are 
adhika in these years. The calculations are based on 
Surya Siddhanta without bija corrections upto 1500 
A. D. arid with these corrections after that year. 

Table 22 — K§aya or decayed months 



Ksaya month 

Adhika months before 

and after the Ksaya 





Kartika, Phalguna 




Kartika, Phalguna 




Asvina, Phalguna 




Kartika, Vaisakha 




Asvina, Caitra 




Asvina, Caitra 




Kartika, Caitra 




Asvina, Caitra 




Asvina, Caitra. 



Ksaya month 

Adhika month 




Asvina, Caitra 




Kartika, Caitra 




Kartika, Phalguna 




Marga., Phalguna 




Kartika, PhlUguna 



L ausa 

Asvina, Phalguna 




Kartika, Vaisakha 




Kartika, Caitra 




Asvina, Phalguna 




Kartika, Vaisakha 




Asvina, Caitra 




Asvina, Caitra 




Asvina, Caitra 




Asvina, Caitra 

It will be observed from the above table that 
according to Surya Siddhanta calculations one ksaya 
month occurs on average after 63 years. But one 
may repeat as soon as after 19 years and as late as 
after 141 years. In rare cases they recur after 46, 65> 
76 and 122 years. 

Intercalary months according to 
modern calculations 

The lunar calendar proposed by the Committee for 
religious purposes is based on the most up-to-date 
value of the tropical year and the correct timings of 
new-moon. As such the intercalary months according 
to these calculations would not always be the same 
as determined from Surya Siddhanta-Cd\cu\aX.ions and 
shown above, The intercalary {mala or adhika) and 
decayed {ksaya) months according to these calculations 
are shown below for Saka years 1877 to 1902. 

Table 23 — Intercalary month according 
to modern calculations. 

Saka A.D 












Kartika & Caitra 
(A.grahayana ksaya 








Proposal of the Committee about the Lunar Calendar 

According to the Siddhantic rules, the lunar 
calendar is pegged on to the solar calendar, and so 
it is the luni-solar calendar with which we are at 
present concerned. It has already been shown that 
the length of the Surya Siddhanta year is greater than 
the year of the seasons {i.e., the tropical year) by 
about 24 minutes. As a result of this the seasons have 



fallen back by about 23 days in our solar calendar. 
The lunar calendar, being pegged on to the Siddhantic 
solar calendar, has also gone out of seasons by about 
the same period, and consequently religious festivals 
are not being observed in the seasons originally 

The solar (saura) month for the religious calendar 

Although the Committee considers that the solar 
year to which the religious lunar calendar is to be 
pegged on should also start from the V. E. day, it felt 
that the change would be too violent ; with a view 
to avoiding any such great changes in the present day 
religious observances, it has been considered expedient 
not to introduce for sometime to come any discon- 
tinuity in this system, but only to stop further -increase 
of the present error. The solar year for the religious 
calendar with Vaisakha as its first taura month should 
now commence when the tropical longitude of the sun 
amounts to 23° 15\ This saura month will determine 
the corresponding lunar months required for fixing the 
dates of religious festivals. The lengths of such 
months, which are also fractional, are stated below, 
giving the lengths according to the Surya Siddhanta 
calculations compared with the corresponding modern 

Table 24— Lengths of Solar months 
of the Religious Calendar. 

Lengths of Months 


Long, of 

Accorditig to Surya 






(1950 A.D.) 




30 d 22 h 

30 d 20 h 55 m 








6 39 








10 53 








8 22 







23 51 








11 51 








23 41 








14 33 








10 40 








12 57 








20 54 








8 33 





5 49 

The. lengths of the months according to the Surya 
Siddhanta are the same as shown . earlier, as the 
same month was used by the S. S. for both the 
purposes. But the modern value, is different from 
that shown before, due to the fact that a different 
point is taken here for the beginning of months. 
The modern value is, however, not fixed for all 
times, but it undergoes slight variation as explained 

The luni-solar calendar by which the religious 
festivals are determined has been pegged on to the 
religious solar calendar starting from a point 23° 15' 
ahead of the V. E. point. As this religious solar 
calendar is based on the tropical year, the luni-solar 
calendar pegged on to it would not go out of the 
seasons to which they at present conform, and so the 
religious festivals would continue to be observed in the 
present seasons and there would be no further shifting. 

The Committee has proposed that the luni-solar 
calendar should no longer be used for civil purposes 
in any part of India. In its place the unified solar 
calendar proposed by the Committee should be used 
uniformly in all parts of India irrespective of whether 
the luni-solar or solar calendar is in vogue in any 
particular part of the country. 


Whenever we wish to define a date precisely we 
have to mention the year, generally current of an era, 
besides the month and the particular day of the month, 
and the week-day. This, enables an astronomer, well- 
versed in technical chronology, to place the event 
correctly on the time-scale. In international practice 
the Christian era is used, which is supposed to have 
started from the birth -year of Jesus' Christ. But as 
mentioned in Chapter II, it is an extrapolated era which 
came in use five hundred years after the birth of the 
Founder of Christianity, and its day of starting may be 
widely different from the actual birthday of Christ, 
about which there exists no precise knowledge. 

In India, nearly 30 different eras were or are used 
which can be classified as follows : — 

(1) Eras of foreign origin, e.g., the Christian era, 
the Hejira era, and the Tarikh Ilahi of Akber. 

(2) Eras of purely Indian origin, list given. 

(3) Hybrid eras which came into existence in the 
wake of Akber's introduction of Tarikh Ilahi. 

Table 27 shows purely Indian eras, with their 
starting years in terms of the Christian era, the elapsed 
year of the era*, the year-beginning, solar, lunar or 
both solar and the lunar as the case may be, the parti- 
cular regions of India where it is current. Inspite of 
the apparent diversity in the ages of the eras, the 
methods of calendarical calculations associated with 
each era are almost identical ; to be more accurate 
only slightly different and follow the rules given in 
either cf the three Siddhantas, Surya, Arya and 
Brahma. The three methods differ but slightly. 

* Generally, but not always the Indian eras have "elapsed 
years". Thus year 1876 of 6aka era would be, if we followed 
the western convention, year 1877 6aka (current). 

C. E. — 40 



The apparent antiquity of certain eras, e.g., the 
Kaliyuga or the Saptar& are however rather deceptive, 
for these eras are not mentioned either in the Vedic 
literature or even in the Mahabharata ( a work of the 
4th to 2nd century B.C. ). The best proof, however, 
that no eras were used in date-recording in ancient 
India is obtained from "Inscriptions" which give 'con- 
temporary evidence' of the method of date-recording 
in use at the time when the inscription was composed. 

In India, the oldest inscriptions so far discovered 
and deciphered satisfactorily are those of the Emperor 
Asoka (273 to 227 B.C.) ; for the earlier Indus valley 
seal recordings have not yet been deciphered and no 
inscriptions or seals which can be referred to the time- 
period between 2500 B.C. (time of Indus valley civili- 
zation) and 250 B.C. ( time of Asoka ) have yet been 
brought to light. Asoka mentions in his inscriptions 
only the number of years elapsed since his coronation. 
No month, week-day or the serial number of the day 
in the month is mentioned. A typical Asokan ins- 
cription giving time references is given in § 5. 5. 

Continuous erak first began to be used in the re- 
cords of the Indo-Scythian kings who reigned in 
modern Afghanistan and North-Western India bet- 
ween 100 B.C. to 100 A.D. 

What is then the origin of the Kaliyuga or Saptam 
era given in Table 27 which go back to thousands of 
years before Christ ? We are going to show presently - 
that they are extrapolated eras invented much later 
than the alleged starting year. 

It is clear from historical records that date-recor- 
ding by an era in India started from the time of the 
Kusana emperors and Saka satraps of Ujjain. But 
India cannot be singled out in this respect, for none 
of the great nations of antiquity, viz., Egypt, Babylon, 
Assyria or later Greece and Rome, used a continuously 
running era till rather late in their history. The 
introduction of the era is connected with the develop- 
ment of the sense of 'History* which came rather late 
to all civilized nations. 

Critical Examination of Indian Eras 

Here we are examining critically the claims of a 
few eras, which are supposed to date much earlier, e.g., 
the Kaliyuga era which is commonly believed to have 
heen introduced in 3102 B.C., the Saptar$i era, and 
the Pa^ava-Kala mentioned by KalWa, the historian 
of Kashmir, who wrote in 1150 A.D., and supposed to 
be dating from 2449 B.C., and others. 

The Saptarsi era commoly known as Lokakala or 
Laukika Kala is measured by centuries and has 27 such 

centuries in the total period of the cycle. Each cen- 
tury is named after a nak§atrai viz., Asvinl, Bharayi, 
etc ; and the'number of years within the century is 
generally mentioned, so that the number of year of the 
era never exceeds 100. This era was in use in 
Kashmir and neighbouring places. In fact this era has 
no relation with the seven gsis (the Great Bear) in the 
sky or with any actual nak?atra division. There is 
difference of opinion as to the beginning of the era. 
According to Vrddha Garga and the Puranas the 
starting year of the tenth century named after Magha 
are 3177 B.C., 477 B.C. and 2224 A.D. of the different 
cycles, when according to Varahamihira the third 
century named Krttika begins. The beginning 
years of Varahamihira s Magha century of the 
different cycles are however 2477 B. C, 224 A. D. 
and 2924 A.D. 

The Pancjava Kala or the Yudhisthira era started 
from 2449 B.C. according to Varahamihira. 

The so-called Yudhisthira era (2449 B.C.) is given 
by Kalhana, chronicler of Kashmir (1150 A.D.), who 
quotes the date from Vrddha Garga, an astronomer 
whose time is unknown. This era also does not occur 
in any inscription or any ancient treatise prior to 
Kalhana (1150 A.D.). Prof. M. N. Saha has shown that 
in the Mahabharata the Krttikas are in many places 
taken as the first of the naksatras and are very nearly 
coincident with the vernal equinox. If we calculate 
the date of the M.Bh. incidents on this basis, the date 
comes out to be very nearly 2449 B.C. 

It, however, niether proves that the incidents 
mentioned in the M.Bh., if they were actual 
occurrences, took place in 2449 B.C., for the epic was 
not certainly put to writing before 400 B.C. as we 
know from a verse already mentioned on p. 226. It is 
inconceiveable to think that the dates could be 
remembered correctly for over 2000 years, when 
writing was in a very primitive state. The astro- 
nomical references in the battle scenes, from which 
certain writers very laboriously deduce the date of 
these occurrences, are most probably later interpola- 
tions, on the supposition that the incidents occurred 
about 2449 B.C. There is no inscriptional record 
regarding the use of Yudhisthira era or Pan(}avakala. 

(a) The Kaliyuga Era 

It is easy to show that the Kaliyuga era which 
purports to date from 3102 B.C. is really an extra- 
polated era just like the Christian era, introduced 
long long after the supposed year of its beginning. 

It is first mentioned by Xryabha{a, the great 
astronomer of ancient Pataliputra, who says that 3600 



years of the Kaliyuga had passed when he was 23 
years old which is Saka year 421 (499 A. D.). It is not 
mentioned earlier either in books or in inscriptions. 
The first mention of this era in an inscription is found 
in the year 634-35 A.D., the inscription being that 
of king Pulakesln II of the Calukya dynasty of 
BadSml, or somewhat earlier in a Jain treatise. It 
was most probably an era invented on astrological 
grounds just like the era of Nabonassar, by Sryabhata 
or some other astronomer, who felt that the great 
antiquity of Indian civilization could not be described 
by the eras then in use (Saka, Chedi or Gupta era), 
as they were too recent. 

What were these astrological grounds ? 

The astrological grounds were that at the beginning 
of the Kaliyuga, the sun, the moon and the planets 
were in one zodiacal sign near the fixed Siddhantic 
Mesadi which according to some authorities is 
( Piscium % but according to others is 180° from Citra 
or a Virginis. This was probably a back calculation 
based on the then prevailing knowledge of planetary 
motion, but has now been found to be totally wrong, 
when recalculated with the aid of more accurate 
modern data on planetary motion. We quote from 
Ancient Indian Chronology, pp. 35 39 by Prof. P. C. 
Sengupta, who has given a full exposition of Burgess's 
views on this point, with recalculations of his own. 

should also bo a total eclipse of the Sun ; but no such 
things happened at that time. The beginning of the 
Kaliyuga was the midnight at UjjayinI terminating the 
17th February of 3102 B.C., according to Surya Siddhanta 
and the ardltanttrika system of Aryabhata's astronomy as 
described in the Khatjdaklmdyaka of Brahmagupta. Again 
this Kaliyuga is said to have begun, according to the 
A.ryabha\iya from the sunrise at Lanka (supposed to be on 
the equator and on the same meridian with Ujjain) — from 
the mean sunrise on the 18th Feb., 3102 B.C. 

Now astronomical events of the type described above 
and more specially the conjunction of the sun and the moon 
cannot happen both at midnight and at the next mean 
sunrise. This shows that this Kaliyuga had an unreal 

The researches of Bailey, Bent ley and Burgess have 
shown that a conjunction of all the 'planets' did not happen 
at the beginning of this Kaliyuga. Burgess rightly 
observes : 'It seems hardly to admit of a doubt that tlie 
epoch (the beginning of the astronomical Kaliyuga) was 
arrived at by astronomical calculation carried backward. 

We also can corroborate the findings of above research- 
ers in the following way and by using the most up-to-date 
equations for the planetary mean elements. 

Now the precession of the equinoxes from 3102 B. C. 
to 499 A. D. or Aryabhata's time works out to have been 
= 49° 32' 39". The mean planetary elements at the beginning 
of the Kaliyuga, i.e., 17th Feb., 3102 B.C., UjjayinI mean 
time 24 hours, are worked out and shown below. We have 

Table 25 — Longitudes of Planets at Kali-beginning. 

Mean Tropical 
longitudes on 
Planet Feb. 17, U.M.T. 

24 hrs., 3102 B.C. 

Moons Apogee 
Moon's Node 

Longitude at the same 
time measured from the 
Vernal Equinox of 499 
A.D,, i.e., Aryabhata's 

The same as assumed in 
the Ardhardtrika system 
at the same time as j 
before and also at next j 
mean sunrise. j 

Error in the assumption 
of Aryabhata and also of 
the modern Surya- 
Siddhanta and the 
KUanda k h ad ya ka . 










+ 8° 









+ 4 










- 3 



















+ 42 


















+ 20 









- 8 






I 331 



+ 28 



" Astronomical Kaliyuga an Astronomical Fiction 9 ' 

At the beginning of the astronomical Kaliyuga, all the 
mean places of the planets, viz., the Sun, Moon, Mercury, 
Venus, Mars, Jupiter and Saturn, are taken to have been in 
conjunction at the beginning - of the Hindu sphere, the 
moon's apogee and her ascending node at respectively a 
quarter circle and a half circle ahead of the same intial 
point. Under such a conjunction of all the planets, there 

added 49° 32' 39" to these mean tropical longitudes arrived 
at from the rules used, so aw to got tho longitudes measured 
from the vernal equinox of Aryabhata's time. 

Hence we see that tho assumed positions of the moan 
planets at the beginning of the astronomical Kaliyuga tvoro 
really incorrect and the assumption was not a reality. But 
of what use this assumption was in Aryabhata's time, i.e., 
499 A.D., is now set forth below. 



Aryabha^a says that when he was 23 years old, 3600 
years of Kali had elapsed. According to his Ardharatrika 
system : 

3600 years=»'l/l200 of a Mahayuga = 1314931.5 days. 
Again according to his Audayika system : 

3600 years =1/1200 of a Mahayuga^ 1314931.25 days. 

Hence according to both these systems of astronomy of 
Aryabhata, by counting 3600 years from the beginning of 
the astronomical Kali epoch, we arrive at the date March 
21, 499 A.D., tjjjayini mean time, 12 noon. The unreality 
of the Kali epoch is also evident from this finding. 
However, the position of mean planets at this time work 
out an given in table 26 below. 

about 57 B. C. Moreover a critical examination of 
inscriptions show the following details about this era. 

The earliest mention of this era, where it is 
definitely connected with the name of king Vikramtf- 
ditya is found in an inscription of one king Jaikadeva 
who ruled near Okhamandal in the Kathiawar State. 
The year mentioned is 794 of Vikrama era, i.e., 737 
A.D. In a subsequent inscription, dated 795 V.E. it 
is also called the era of the lords of Mslava. So the 
Vikrama era and the era of Malava lords are one and 
the. same. Tracing back, we find the Malavagana era 
in use by a family of kings reigning at Mandasor, 
Rajputana between the years 461-589 V.E., as feuda- 

Table 26 — Longitudes of Planets at 3600 Kaliyuga era. 
Date : March 21, 499 A.D Ujjayini Mean Midday. 

Mean Long. 

Mean Long. 

Mean Long. 

. Error in the 









0° 0' 


0° 0' 



42' 5" 

+17' 55" 


280 48 

280 48 


24 5a 

+23 8 

Moon's Apogee 

35 42 

35 42 


24 38 

+17 22 

Moon's Node 

352 12 

352 12 


2 26 

+ 9 34 





9 51 

+2° 50' 9" 


356 24 

356 24 


7 51 

+16 9 


7 12 

7 12 


52 45 

+ 19 15 



187 12 


10 47 

+ 1 13 


49 12 

49 12 


21 13 

+50 47 

It is thus clear that the beginning of the Hindu 
astronomical Kaliyuga was the result of a hack calculation 
wrong in its data, and was thus started wrongly. 

It is also established that the astronomical Kaliyuga- 
reckoning is a pure astronomical fiction created for facilita- 
ting the Hindu astronomical calculations and was designed 
to be correct only for 499 A.D. This Kali-reckoning 
cannot be earlier than the date when the Hindu scientific 
Siddhantas really came into being. As this conclusion 
<jannot but be true, no Sanskrit work or epigraphio 
evidences would be forthcoming as to the use of this 
astronomical Kali-reckoning prior to the date 499 A.D". 

(b) The Vikrama Era 

The Vikrama Era is widely prevalent in Northern 
India? excepting Bengal, and used in inscriptions from 
the ninth century A.D. Let us probe into its origin. 

In popular belief, the Vikrama era was started 
by king Vikramaditya of Ujjain who is claimed to 
have repelled an attack on this famous city by Saka 
or Scythian hordes about 57 B. C. and founded an 
era to commemorate his great victory. 

Unfortunately no historical documents or inscrip- 
tions have yet been discovered showing clearly the 
existence of a king Vikramaditya reigning at Ujjain 

tories to the Imperial Guptas ( 319-§50 A.D. ). They 
call it not only the era of the Malava tribe* but also 
alternatively as the Krta era. A number of inscrip- 
tions bearing dates in the Krta era have been found in 
Rajasthan, and the earliest of them goes back to the 
year 282 of the Krta era (The Nandsa Yupa inscription 
described by Prof. Altekar, Epigraphia Indica, Vol. 
XXVII, p. 225). 

From these evidences, it has been concluded by 
historians that the earliest name so far found of this 
era was Krta. What this means is not clear. Then 
between 405-542 A.D., it came to be known as the 
era of the Malava tribe and was used by the Verma 
kings of Mandasor, Rajputana, though they were 
feudatories of the Gupta emperors (319-550 A .p.). Its 
association with king Vikrama is first found in the 
year 737 A.D., nearly 800 years after the supposed 
date of king Vikrama. Its use appears to have been 
at first confined to Kathiawar and Rajasthan, for the 
whole of Northern India used between 320 A.D. to 
600 A.D., the Gupta era, which fell into disuse with 
the disappearance of the Gupta rule in 550 A.D. For 
a time. Northern India used the Harsa era introdu- 
ced by the emperor Harsa Vardhana (606 AJD.), but 
when the Gurjara-Pratihars, who came from 



JUjasthan, conquered the city of Kanauj about 824 
A.D., they brought the Vikrama era from their original 
home, and it became the current era all over northern 
Inciia except the eastern region, and was used by all 
Rajput dynasties of medieval times. 

The months of the Vikrama era are all lunar, and 
the first month is Caitm. The months begin after the 
full-moon but the year begins 15 days after the full- 
moon of Phalguna, i.e. after the new-moon of Caitra* 
But for astronomical calculations, it is pegged on to a 
solar year, which starts on the first of solar Vaisakha, 
theoretically the day after the vernal equinox. The 
Vikrama era is current also in parts of Gujrat, but 
there the year begins in KSrttka and the months are 
amanta, which corresponds to the Macedonian month 
of Dios, and the epoch is just six months later. 
Thus the western and northern varieties of the 
Vikrama era follow respectively the Macedonian and 
Babylonian reckonings (see § 3.3), the year of starting 
is 255 years later than that of the Seleucidean era. 

The conclusion is that the champions of the 
Vikrama era have still to prove the existence of king 
Vikrama of Ujjain. Early inscriptions show that the 
method of date-recording is not typically Indian as in 
the Satavahana inscriptions but follow the Saka-KusSna 
method, which fpllows the contemporary Graeco- 
Chaldean method. It was therefore a foreign recko- 
ning introduced either by the Greeks or Sakas, or 
an Indian prince or tribe who had imbibed some 
Graeco-Chaldean culture, but was adopted by the 
Malava tribes who migrated from the Punjab to Rajas- 
than about the first century B.C. The association 
with a king Vikrama occured 800 years later, and is 
probably due to lapse of historical memory, for the 
only historical king VikramSditya who is known to 
have crushed the Saka power in Ujjain, was king 
Candragupta II of the / Gupta dynasty (about 395 
A.D.). Before this, the Saka dynasty in Ujjain had 
reigned almost in unbroken sequence from about 100 
A.D. to 395 A.D., and ^had used an era of their 
own, later known as the 'Saka' era. All the Gupta 
emperors from Samudragupta, had an "Aditya" title, 
and many of them had the title "Vikramaditya" so 
that the Gupta age was par excellence the age of 
Vikramadityas. But all the Gupta emperors use in 
their inscriptions the family era called the Guptakala 
which commemorated the foundation of Gupta empire 
(319 A.D.). The association of the Malava era with king 
VikramSditya, and assignment of king VikramSditya 
to Ujjain, was due to confusion of historical memory 
not infrequent in Indian history. It may be' mentioned 
that the Vikrama era is never used by Indian astro- 
nomers for their calendaric calculations, for which 
puapose the Saka era is exclusively used. 

(c) The Saka Bra 

Hie Saka Era is the era par excellence which has 
been used by Indian astronomers all over India in their 
calculations since the time of the astronomer Varaha- 
mihira (died 587 A.D.) and probably earlier. The 
Indian almanac-makers, even now, use the Saka era 
for calculations, and then convert the calculations to 
their own systems. 

This era is extensively used over the whole of India 
except in Tinnevelly and part of Malabar, and is more 
widely used than any other era. It is also called Saka 
Kala, Saka Bhtlpa Kala, Sakendra Kala, and Salivahana 
Saka and also Saka Samvat. Its years are Caitradi for 
luni-solar reckoning and Me$adi for solar reckoning. 
In the luni-solar reckoning the months are purnirnanta 
in the North and amanta in Southern India. The 
reckoning of the Saka era begins with the vernal equi- 
nox of 78 A.D., and is measured by expired years, so 
the year between the vernal equinox of 78 A.D. to that 
of 79 A.D. is zero of Saka era. In some pancangas or 
Southern India the current year is however seen to be 
used instead of the elapsed year, where the number of 
year of the era is one more than the era in general use 
But we are not yet sure about the origin of this 
era. It has been traced back to the Saka satraps of 
Ujjain, from the year 52 (130 A.D.) to the end of the 
dynasty about 395 A.D. But in their own records, 
they merely record it as year so and so, but there is 
not the slightest doubt that the era used by them 
subsequently became known as the Saka era (vide § 5.5). 
The Old and the New Saka era. 
The dates given by different authorities about the 
starting year of the old Saka era mentioned in § 5.5 
vary from 155 B.C. to 88 B.C. as given below : 
Konow ; 88 B.C. (date of death of Mithradates II, the 
powerful Parthian emperor who is 
said to have subjugated the Sakas). 
Konow has proposed a number of other dates. 
Jayaswal : 120 B.C. : 

Herzfeld : 110 B.C. : Settlement of the Sakas in 

Seistan by Mithradates II. 
Rapson : 150 B.C. : Establishment of the 8aka 

kingdom of Seistan. 
Tarn : 155 B.C. : Date of settlement of the Saka 

immigrants in Seistan by 
Mithradates I. 
Recently Dr. Van Lohuizen de Leeuw has discus- 
sed the starting point of this era in her thought-provok- 
ing book 'The Scythian Period of Indian History*. She has 
rejected all the above dates, and fixed up 129 B.C. as 
the starting date of the old Saka era. She identifies this 
year as the one in which the Sakas, descending from 
the Trans-Oxus region, attacked the Parthian empire 


in which the Parthian emperor Phraates II was defea- 
ted and killed, and the rich province of Bactna was 
occupied by the Sakas. They founded an era to com- 
memorate their victory over the Parthians which their 
successors took to India, as they expanded and put an 
end to the Bactrian Greek principalities in Afghanistan 
and north-west Punjab. She suggests that the old 
Saka era was also used by the Kusanas, who were 
after all a Sakish ruling tribe, but from the time of 
Kaniska with hundreds omitted. 

Dr. M. N. Saha has supported this theory in its 
main features, but he thinks that the era was founded 
in 123 B C , for he shows from historical records that 
I the Sakas assailed Bactria first in 129 B.C. and entered 
! into a seven year conflict with the Parthians, and 
! finally conquered Bactria in 123 B.C., when the Par- 
thian emperor Artabanus II, was defeated and killed. 
Probably the Sakas then founded their era. This Was 
also called the era of Azes. Dr. Van Lohuizen de 
Leeuw has accepted Sana's suggestion. 

This hypothesis, though not finally settled appears 
to- have , a good deal of probability, for the following 
reasons : 

Dr. Saha points to the fact that Indian classics, 
which can be dated from the third century B.C. to the 
second century A.D., mentions three races in what is 
modern Afghanistan and N. W. India, viz., the Sakas, 
the Yavanas, and the Pallavas, who attained to the 
status of ruling races. The order in which they are 
mentioned denotes correct chronological sequence, for 
they are arranged in the order of their chronological 
appearance in history, the gakas being mentioned as a 
subject race in Darius's inscription (518 B.C.). But 
the Yavanas (Greeks) were the first to attain the status 
of a ruling race, from 312 B.C., the date of foundation 
of the Seleucid empire, whose power in the west was 
overthrown by the Parthians, or Pehlevis (Pallavas of 
Indian classics) in 248 B.C. 

Both these ruling races of Yavanas and Pallavas 
used eras of their own, viz., the Seleucidean era from 
312 B.C., and the Parthian era from 248 B.C. Did the 
third race, the Sakas who were the last to attain 
status of a ruling race ever use an era of their own ? It 
would be surprising if they did not, for it became the 
fashion for all races, who attained the status of ruling 
people, to have eras of their own. The early Sakas, 
as their records show, were deeply influenced by their 
neighbours to the west, viz., the Parthians who adopted 
Greek culture, and their coin-records show that they 
also adopted Greek culture, and therefore most 
prbbably. the Graeco-Chaldeah method of date 


The points given in § 5.5 and above may be 
summarized as follows : — 

(a) The Sakas starting from Central Asia attacked 
the Parthian empire in 129 B.C., and overcame 
Parthian resistance by 123 B.C. It is very probable 
that they started an era to commemorate their 
accession to power in Bactria from 123 B.C. They used 
Macedonian months and Graeco-Chaldean methods of 
calendaric calculations as prevalent in the Seleucid 
and Parthian dominions. Probably the era was some- 
times named after Azes, who was probably their leader. 
But this Azes is not to be confounded with later 
Azes I or Azes II, who reigned in Taxila between 40 
B.C. and 20 B.C. Within the first 200 years of its 
starting/the era was alternatively called the Azes era. 

(b) This Saka era ( known to archaeologists as the 
old Saka era ) was used by the Saka emperors and Saka 
satraps in their Indian territories, but the time- 
reckoning began to ba gradually influenced by Indian 
customs. They began to use Indian months alter- 
natively with Macedonian months and Pur'nimanta 
months in place of Am&nta months. During the first 
200 years, the hundreds were sometimes omitted, in 
the use of the era. 

(c) The so-called Kaniska era is nothing but the 
old Saka era with 200 omitted. 

(d) The Saka era was used by the house of Castana 
of Ujjain with 200 omitted, but gradually they forgot 
the origin of the era and continued their own reckoning 
without further omission of hundreds upto the end of 
the Saka satrapal rule over UjjainI about 395 A.D. As 
the early Indian astronomers were mostly of foreign 
origin (viz. Sakadvlpi Brahmana) the astronomical 
reckonings necessary for compiling the calendar were 
carried out using the Saka era and Graeco-Chaldean 
astronomy. The blending of Graeco-Chaldean 
astronomy as known about the early years of the 
Christian era with older Indian calendarica^ features 
formed the basis of Siddhanta Jyotisa. The Sakadvlpi 
Brahmins also brought to India horoscopic astrology 
using the Saka era exclusively in horoscopes, a custom 
which has persisted to this day. These facts explain 
the pre-eminence of the Saka era. 

(d) Other Eras 

Buddha Nirvana Era .—The Buddhists of Ceylon 
have been using since the first century B.C. the 
Buddhist Nirvana* era, having its era-beginning in 544 
B.C. This era has not however been found in use on 
the Indian soil, except for a solitary instance in 
an inscription of Asokachalla Dev found at Gaya 
dated in the year 1813 of the Buddhist Nirvana 



era — 1270 A.D. Most of the antiquarians however 
put the date of Nirvana in 483 B.C. The origin of 
the Buddha Nirvana era used in Ceylon has not yet 
been satisfactory explained. 

The Gupta Era : — This era was clearly ] established 
by the founder of the Gupta dynasty (Candragupta I) 
to commemorate the accession to imperial power of 
his family, about 319 A.D., and was in vogue over the 
whole of Northern India from Saurashtra to Bengal 
during the days of their hegemony (319 A.D.-550 A.D.). 
After the decay of their empire, the era was continued 
by their former vassals, the Maitrakas of Vallabhi and 
was in use in parts of Guzrat and Rajputana up to 
the thirteenth century. Its use in Bengal was discon- 
tinued from about 510 A.D. with the disappearance 
of Gupta rule first in South Bengal, then over the 
whole of Eastern India. In the Uttar Pradesh (ancient 
Madhyadesa), it was driven out by the Harsa era, 
which had a short period of existence, 606-824 A.D., 
when the city of Kanauj was occupied by king 
Nagabhata of the PratihSr dynasty, who hailed from 
Rajasthan. The Pratihars brought with them the 
Vikrama era, . which had been current in Rajasthan, 
and this became the great era of the north, used by 
all medieval Rajput dynasties, except those belonging 
to the eastern region. 

Eras in Eastern India 

Most parts of Bengal were under the Gupta 
emperors, and used the Gupta era during their 
hegemony (319-510 A.D.). But Gupta rule disappeared 
as mentioned above from major parts of Bengal from 
<ra. 510 A.D., and the subsequent dynasties including 
the Pala emperors ( 750 A.D —1150 A.D. ) used regnal 
years in their inscriptions for four hundred years of 
their rule. The Saka era in Bengal appear to have been 
introduced by the Sena dynasty which replaced the 
Palas ; the Senas were migrants from the south 
{ Karnata-Ksatriyas ), where they were familiar with 
the Saka era, but it was not used in royal records 
which continued to use regnal years. The Vikrama 
Samvat never became popular in Bengal, or Eastern 
India. After Mohamedan conquest, Bengal was left 
without an era. For official purposes, Hejira was 
used, But the learned men used the Saka era, and the 
common people in certain parts used a rough reckoning, 

called Parganati'AMa, reckoned from the time of 
disappearance of Hindu rule. 

After the introduction of Tarikh Ilahi, the people 
of Bengal began to use the Sarya Siddhanta reckoning, 
and the solar year. The Bengali San had thus a 
hybrid origin ; to find' the current year of the Bengali 
San, we take Hejira year elasped in 1556, i.e., 963 and 
add to it the number of solar years. Thus 1954 
A. D. is 963 A.D. + (1954 -1556) -1361 of Bengali San, 

Other hybri eras 

A number of other hybrid eras formed in a similar 
way to Bengali San is mentioned in the table (No. 27) : 
Amli and Vilayati in Bengal and Orissa, the various 
Fasli or harvest years in Bengal, Deccan, and 

All the other eras mentioned as hybrid in the 
chart were formed in a similar way, and the slight 
differences are due to mistakes in calculation, or 
differences in the time of introduction. While the 
Bengali San has Mesadi as year-beginning, others 
have taken the year-beginning to be coincident with 
some important mythical event of local provenance, 
e.g., the year-beginning of the Amli era used in 
Orissa, viz., the 12th lunar day of the light half of the 
month of Bhadra is said to represent the birth date 
of king Indradyumna, the mythical king who is said 
to have discovered the site of modern Puri. The 
great temple of Puri was actually built by king 
Anyanka Bhim Dev of the Ganga dynasty about 1119 
A.D., and kings of this dynasty who held sway in 
Orissa from 1035-1400 A. D, used the Ganga era, 

The Kollam era prevalent in the Malayalam 
countries is of obscure origin. The year of this era 
is known as the Kollam Anclu. The era is also called 
the Era of Parasurama, and is said to have omitted 
thousands from their previous reckonings. In South 
Malabar it begins with the solar month Simha and 
in North Malabar with the solar month Kanya. 
The era started from 825 A.D. 

The Jovian cycle : In Southern India the years are 
named after the name of the Jovian year and so it also 
serves the purpose of an era of a short period, viz., 60 
years, after which the years recur. Details about 
Jovian years will be found in Appendix 5-E. 

[ 258 





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The Seasons 

We have seasons because the celestial equator is oblique 
to the sun's path (or the ecliptic), or in modern parlance, 
the axis of rotation of the earth is not perpendicular to its 
orbit, but inclined at an angle of 66*°. This causes varying 
amounts of sunlight to fall on a particular locality through- 
out the year. If the earth's axis were perpendicular to the 
ecliptic, in other words the obliquity were zero, every 
portion of the earth from the equator to the pole would 
have had 12 hours of sunlight, and 12 hours of shade. 
There would have been no seasons on any part of the earth, 
just as we have now for places on the earth's equator, where 
we have no variation of season throughout the year, because 
the day and night are equal for all days of the year. 

It can be proved from spherical trigonometry that the 
duration of sunlight for a place having the latitude <t> is 
given by 

12+tV Sin" 1 ( tan <p tan S ) hours, 
where 8= declination of the sun on that day ; 8 being 
counted positive when it is north of the equator, and 
negative when south. 

If S is negative, i.e., when the sun is south of the 
equator, the second term of the above equation is negative, 
and daylight will be of less than 12 hours' duration. 

This holds up to the latitude of ^— € = 66*°, i.e., the 

beginning of the arctic zone. Between the arctic circle 
and the north pole, the sun will remain constantly above 
the horizon more than twenty-four hours for several days 
together during the year. Thus at a place on 70° north 
latitude, the continuous day is observed for 64 days from 
21st May to 24th July, at 80° north latitude it is for 133 
days from 17th April to 28th August, at the north pole it 
is for six months from 21st March to 23rd September. - 

For a person on the north pole, the sun will appear on. 
the horizon on the vernal equinox day, and will go on 
circling round the sky parallel to the horizon and rising 
every day a little up, till on the solstitial day, he attains 
the maximum altitude, viz., 23° 27'. After that the sun 
will begin to move down and on the day of autumnal 
equinox, will pass below the horizon. Thus for six 
months, from 21st March '(V.E.) there will be continuous 
day for a person on the north pole, and from the 23rd Sept, 
(A.B.) to the. next 21st March (V.E.), there will be a 
continuous night for six months. 

The position described above is for the northern hemis- 
phere, viz.j for those dwelling north of the equator. In the 
southern hemisphere the position is just reversed ; when 
the day is longer in the northern hemisphere, it is shorter 
in the southern hemisphere. 

The amount of daylight received at any place determines 
the season. When we have maximum sunlight, we have 
the hot season. When we have minimum sunlight, we shall 
have winter. The other seasons come in-between. Bain, 
frost, etc., are secondary effects produced by varying 
amounts of sunlight, and of the atmospheric conditions 
stimulated by the sunlight received. The sun is the sole 
arbiter of the seasons. 

Hence the definitions of seasons as given by the ancient 
astronomers, whether Western and Indian, which base them 
on the cardinal days of the year, are the only correct 
definitions. A system which deviates from this practice is 

The majority of the Indian calendar makers have not, 
however, followed this definition. The reason is more 
psychological than scientific. For along with astronomy, 
there has been also a growth of astrology which has fixed 
up its canons on the basis of a fixed zodiac commonly known 
as the Nirayana system. The effect of this will be clear 
from the following example. 

The winter season (ki&ira) begins on the winter solstice- 
day which date is also marked in all the Siddhdntas by 
sun's entry (safnkranti) into Makara. This event occurs on 
the 22nd December. But the Indian calendar makers, 
following the nirayana system, state that the Makara 
Safnkranti happens not on the 22nd December but on the 
14th January and the winter season also begins on that 
date. Similar is the case with other seasons also. The result 
is that there is a* clear difference of 23 days in the reckoning 
of seasons. The later Hindu savants tried to reconcile the 
two points of view by adopting a theory of trepidation, 
which after Newton's explanation of precession, has been 
definitely shown to be false. It is therefore absolutely 
wrong to stick to the nirayana system. 

It is however refreshing to tfnd that a few Indian 
savants have definitely stood against the false nirayana 
system. The earliest were MuSjala Bha^a (932 A.D.), a 
South Indian astronomer and Prthudaka Svami (950 A.D.), 
who observed at Kuruksetra. One of the latest was Mm. 
Bapudev Sastri, 0. I. R, Professor in the Sanskrit College, 
Banaras, who wrote in 1862, as follows : 

"Since the nirayana safnkrantis cannot be determined 
with precision and without doubt and since the nirayana 
raiis have no bearing on the ecliptic and its northern and 
southern halves, we must not hanker after nirayana system 
for the purposes of our religious and other rites. We must 
accept say ana and our religious and other rites should be 
performed in accordance with the say ana .system". 

0. R. -41 




It is not generally known that another great man who 
probably felt that the nirayaria system gave us wrong 
seasons, was Pandit Ishwar Chandra Vidyasagar. We 
learn from his biography that he had a course in Indian 
astronomy while he was a student of the Sanskrit College, 
Calcutta about 1840. Before him, the Vasanta r Spring 
insisted of the months Madhu and Madhava, i.e., Caitra 
and Vai&akha, as in other parts of India. But from 1850, 
Vidyasagar began to bring out text books in Bengali in 
which he retarded the seasons by a month, e.g., he said that 
the spring consists of Phalguna and Caitra, and no one 
questioned it. So in Bengal, as far as popular notion goes, 
Vasanta season starts on Feb. 12, while in other parts it 
starts on March 14, a month later, while the correct 
astronomical date according to Hindu Siddhantas is Feb. 19. 
Bengal thus commits a negative mistake of 7 days while 
other parts of India has a positive mistake of 23 days. 

The position in respect of all the seasons is stated 
below : 

Sun's longitude Correct date Present date 

Vasanta ( - ) 30° to 30° Feb. 19 to Apr. 19 Mar. 14 to May 13 

Grisma 30° to 90° Apr. 20 to June 20 May 14 to July 15 

Varsa 90° to 150° June 21 to Aug. 22 July 16 to Sep. 15 

Sarat 150° to 210° Aug. 23 to Oct. 22 Sep. 16 to Nov. 15 
( Autumn) 

Hemanta 210° to 270° Oct. 23 to Dec. 21 Nov. 16 to Jan. 12 
(Late Autumn) 

Sisira 270° to 330° Dec. 22 to Feb. 18 Jan. 13 to Mar. 14 

In continuing to follow the nirayana system, the Hindu 
calendar makers are under delusion that they are following 
the path of Dharma. They are aerially committing the 
whole Hindu society to Adharma. 

The period covering the north-ward journey of the sun 
was known in Indian astronomy as the UttarayaT^a 
i.e., north- ward passage and it consisted of the Winter, 
Spring and Summer. It is the period from winter solstice 
to summer solstice, and vice-versa, the period from summer 
solstice to winter solstice was known as the Daksii^ayana, 
i.e., southward passage and it consisted of Rains, Autumn 
and Hemanta. 

The names of months given in the second column of 
Table No. 28 are found first in Taittiriya Safnhita, and they 
are tropical, because they attempt to define the physical 
characteristics of the months. 

Madhu means. 'Honey' and the name indicates 

that the month was pleasant like honey. 

Madhava... means - Honey like' or 'Sweet one'. 

The names are thus expressive of the pleasantness of the 
spring season. 

The figures in the third column of the table below denote 
the angular distance of the sun from the astronomical first 
point of Aries (the V.E. point) indicating the beginning of 
the month. 

The two months constituting the 'Spring Season' would 
thus include the day from Feb. 19 or 20 to April 19 or 20. 
The Vernal Equinox day (March 21) would be just in the 
middle. The same is the case with other seasons each of 
two months. 





Late Autumn! 








Table 28. 

1 -30° 

J o 

1 30 

J 60 

) 90 
J 120 

1 150 
J 180 

\ 210 
f 240 

Honey or sweet spring 
The sweet one 





270 Penance, mortification, 

300 Pain (produced by heat) 

These names were seldom used by the common people, 
but they were very popular with poets. 

The figures in the second column of table No. 29 
denote the angular distance of the sun on the ecliptic, the 
origin being the first point of Aries, We have described 
in § 4.5 how an idea of the ecliptic was derived from night 
observations of the sky and observation of eclipses, and 
how it came to be used as a reference plane from very 
ancient times. 

The Indian definition of the seasons, though was based 
on the cardinal days, was different from the definition of the 
westerners who divided the year into four seasons each of 
three months Winter, Spring, Summer and Autumn, starting 
from*the four cardinal days. The ancient Indians divided 
the year into six seasons each of two months as given in 
the table below. The spring season did not start with the 
vernal equinox, as already stated but a month earlier and it 
was extended a month later, and so for every season. 

Table 29. 

Indian Seasons Tropical Month-names Lunar Month-names 

Spring (-30° to 30°) 
Summer (30° to 90°) 
RainB (90° to 150°) 
Autumn (150P to 210°) 
Late Autumn 

(210 5 to27(P) 
Winter (270°to330e) 

Madhu & Madhava 
&ukra & f§uci 
Nabhas & Nabhasya 
Isa & Orja 

Sahas & Sahasya 
Tapas & Tapasya 

Caitra- Vaisfikha 
Jyaig^ha- Agatha 


The early Greek astronomers have left records about 
their successive attempts to measure the length of the year 



correctly. It is now known that they all used the gnomon. 
Measures of the length of the different seasons and of the 
year by some of their eminent astronomers are 'given in the 
table (No. 30) below. 

The Chaldeans must have also measured ' the length ot 
the year by the same method, either somewhat earlier or 
simultaneously with the early Greeks, but their names, 
excepting those of a few have not survived. But if in 
reality, the nineteen-year cycle was of. as early as 747 B.C., 
they must have arrived at a correct length of the year much 
earlier than any other nation. 

The Length of the Seasons : The lengths of seasons were 
found exactly in the same way as in the case of the 
year, e.g.> in the case of Spring, by counting the number of 
days from the day next to the yernal equinox day to the 
summer solstice day. The number would be variable from 
year t6 year, but a correct value was found by taking the 
observations for a number of years and taking the mean. 
The lengths obtained by early astronomers are : 

Table 30. 

Spring Summer Autumn Winter Total 
days days days days days 
Chaldean ... 94.50 92.73 88.59 89.44 365,26 

Euctemon(432B.C) 93 90 90 92 365 

Calippos (370B.C) 94 92 89 90 365 

Correct values 

for 1384 B.C. ... 94.09 91.29 88.58 91.29 365.25 
The ancients early discovered that the seasons were of 
unequal length, but they were ignorant of the physical 
reasons. These exact definitions of seasons, both in India 
and in the West, were arrived at very early, and are very 
important for accurate calendar-making ; but the true 
meaning of these definitions were forgotten in the succeed- 
ing periods in India. 

In European astronomy, which is derived from Graeco- 
Chaldean astronomy, we have : 

Spring 0°— 90° from V.E. to S.S. 

Summer 90°— 180° " S.S. to A.E. 
Autumn 180°— 270° " A.E. to W.S. 
Winter 270°— 360° " W.S. to V.B. 
According to this scheme, the Bainy season consisting 
of months of Nabhas and Nabhasya formally set in when 

the sun crossed the summer solstice (June 22), as is evident 
from the lines in Kalidasa's MeghadUta or Cloud-Messenger. 

Pratyasanne Nabhasi dayitajivita lambanarthi 
Jimutena svakusalamayim harayi^yan pravrttim. 

Translation : When the month of Nabhas was imminent, 
( just marking the onset of monsoon ), etc.** 

Or in the Bamayana, Ayodhyakay><ia 

Udaggatva-abhyupabrtte paretacaritam disam 
Abrnvana disab sarvat snigdha dadrsire ghanah. 

Translation : When the sun just reversed its motion after 
going (continuously) to the north, and began to proceed in 
the direction inhabited by departed souls (dak?inayana), the 
whole sky was overcast with clouds (i.e., the monsoon set 

WiDter solstice set in with the month of Tapas, - which 
means penance. The winter solstice as mentioned above 
was the time from which the yearly sacrifices started. 

The month names in the last column of table (No. 29) 
are 'lunar', but they were linked to the solar months. They 
are now in universal use all over India to denote 
solar as well as lunar months ; but the two varieties are 
distinguished by the adjectives 'Solar' or 'Lunar*. 

Both the European and Indian definitions of seasons 
are scientific as they are based on the cardinal days. The 
difference in nomenclature is trivial. 

The Length of the Year : The length of the year, as 
mentioned earlier, must have been found by counting the 
number of days from one equinox to another, or one solstice 
to another. 

In actual practice, the number of days of the year, 
counted in this way would vary between 365 and 366. In 
the early stages, the length of the year was whole-numbered, 
but Indians of Vedanga Jyotisa period had a year of : 366 
days. Later when they came to a rigorous definition of the 
year, they realized that the number of days was not whole, 
but involved fractions. Probably the attempt at determin- 
ing the exact length of the year involving fractional 
numbers was obtained by adding up the lengths for a 
number of years, and taking the mean. 


The Zero-point of the Hindu Zodiae 

The Zero-point of the Hindu Zodiac : By this is meant 
the Vernal Equinoctial Point (first point of Aries) at the 
time when the Hindu savants switched on from the old 
Vedaiiga-Jyoti$a calendar to the Siddhantic calendar (let 
us eel this the epoch of the Siddhanta- Jyotisa or S. J.). 
There is a wide spread belief that a definite location can be 
found for this point from the data given in the Surya- 
Siddhanta and other standard treatises. This impression is 
however wrong. 

Its location has to be inferred from the co-ordinates 
given for known stars in Chap. VIII of the SUrya Siddhanta. 
From these data Diksit thought that he had proved that it 
was very close to Bevati (C Piscium) ; but another school 
thinks that the autumnal equinoctial point (first point of 
Libra) at this epoch was very close to the star Citra (Spica, 
< Virginis), and therefore the first point of Aries at the 
epoch of S.J was 180° behind this point. The celestial 
longitude in 1950 of f Piscium was 19° 10' 39" and of 
* Virginis was 203° 8' 36". The longitudes of the first 
point of Aries, according to the two schools therefore 
differ by 23° 9'(-)l9° 11'= 3° 58' and they cannot be 
identical. Bevati or f Piscium was closest to T (the V.E. 
point) about 575 A.D., and Citra or < Virginis was closest 
to ^ (the A.E. point) about 285 A.D., a clear difference 
of 290 years. 

Thus even those who uphold the nirayarta school are 
not agreed amongst themselves regarding the exact location 
of the vernal point in the age of the Sftrya-Siddh&nta 
and though they talk of the Hindu zero-point, they do 
not know where it is. Still such is the intoxication 
for partisanship that for 50 years, a wordy warfare 
regarding the adoption of either of these two points as the 
zero-point of the Hindu zodiac has gone on between the 
two rival factions known respectively as the Bevafl-Pak§a 
and Citr3,-Pak$a, but as we shall show the different parties 
are simply beating about the bush for nothing. 

Chapter VIII of the S.S gives a table of the celestial co- 
ordinates (Dhruvaka and Vik$epa) of the junction-stars 
(identifying stars) of 27 asterisms forming the Hindu lunar 
zodiac. It is agreed by all that these co-ordinates must 

have been given taking the position of the V.E. point at the 
observer's time as. the fiducial point. It is possible to 
locate it, as Burgess had shown in his edition of the S.S., if 
with the aid of the data given, X, i.e., celestial longitude of 
the junction- stars in the epoch of S.J. is calculated, and 
compare it with the X of the same stars for 1950. Let the 
two values of X be denoted by \± and X a , \ x being the value 
at the epoch of S. J., X t for the year 1950. ThenX a -X x 
should have a constant value, which is the celestial 
longitude of the V.E. point at the epoch of the S.J. on the 
assumption that they refer to observations at a definite 
point of time. The following is a short exposition of 
Burgess's calculations. 

The S.S. gives the position of the junction-stars in 
terms of Dhruvaka and Vik$epa, two co-ordinates peculiar 
to Sury a- Siddhanta. Their meaning and relation to the 
usually adopted co-ordinates is illustrated by means of 
fig, 27 and for convenience of the reader, the standard 


Kg. 27 

designations, symbolisms used for the different systems of 
celestial co-ordinates along with their Hindu equivalents 
are shown in the table below : 

Table 31 — Siddhantic designation of celestial co-ordinates. 







Celestial longitude 




As in Surya Siddhanta 

Celestial latitude 



Used by Bhaskara 

Eight Ascension 









As in Surya Siddhanta 

Polar longitude 





Polar latitude 








With the aid of spherical trigonometry, the following 
relations may be deduced : — 

sin £ = sin d sin B ...(l) 

sm (X— I)— tan j8 cot B \ ((X \ 
or tan (X-l)=tan d cos B J KA) 
where, cot \B=cos I tan « (3) 

The objective is to deduce the values of X and j8 of a 
star whose Z, d are to be found from Chap. VIII of S.S. 
As the formulae show, the key angle is B, which is deter- 
mined with the aid of relation (3). Then (l) gives us j3 
and (2) gives us X— I. So X and J8 for the star are found. 

Proceeding in this way, Burgess calculated the values 
of X and of the junction-stars given in the S.S. We have 
•hacked these calculations. These are reproduced in table 
No. 32 on pp. 264-65 in which : 

Column 1 gives us the serial no. of the naksatra. 

* 2 " their names. 

* 3 " " the name of the junction star as 

accepted ( see however later 

m 4 " " the magnitude of the star. 

" 6 " " the celestial longitude of the star 

in 1950 from data given in a 
modern Ephemeris. 
6 " the celestial latitude of the star. 

* 7 " " the dhruvaka or polar longitude 

as given in S.S. 
" 8 " " viksepa or polar latitude as given 

in S.S. 

" 9 »* " the celestial longitude of junction 

star, from the data given in the 
S.S. converted with the aid of 
the formula mentioned above. 
. " 10 " " celestial latitude similarly conver- 
ted from data given in S.S. 

" 11 " " the difference in celestial longitude 

of the star for 1950 over that 
for the time of S3. 

" 12- " " the difference between the lati- 

It iB evident that 0-/3' ought to be zero for all stars, 
which is however not the fact as may be seen from the 
table. In the time of the S.S., the observations cannot be 
expected to have been very precise. But yet we cannot 
probably hold that an identification is correct when the 
difference is too large. We are therefore rejecting all 
identifications where j8 — 0' exceeds 2°. Probably these stars 
have not been correctly identified from the description 
given for them, or the co-ordinates given in the Surya- 
Siddh&nta were erroneously determined or wrongly handed 
down to us. In the case of other stars, we find that X a — X x 
is 16° 47' (or 10° 52'), 16° 58' and 26 u ' 18' for three stars. 
We are also rejecting these three identifications. This 
leaves us with the identification of 16 stars as somewhat 

certain. The values of X a — Xi are in three groups as 
follows : 

Group 1. 

No X.— Xi 

-.2 22° 53' 

8 22 1 

9 22 57 

14 22 21 

Group 2. 




4 20 57 



21 21 


Group 3. 



20 8 

20 47 

19 40 

18 58 



1-22° 33' 



h 20° 48' 



19 21 

h 19° 9' 

(N.B. In giving the Dhruvaka and Viksepa, the S.S. 
uses a unit called Liptika, which means a minute of arc. 
This is traced to Greek "Lepton'*. Prof, B. V. Vaidya 
thinks that some of the figures for asterisms, as they are 
given by cryptic Sanskrit words, have not been properly 

We are not aware how the Hindu savants determined 
the dhruvakas and vik§epas. It appears that they had a 
kind of armillary sphere with an ecliptic circle which they 
used to set to the ecliptic with the aid of standard stars 
like Pu$ya (S Gancri), Magha {<Leonis) Citra (< Virgin**}, 
Visakha {< Libra) and l^atabhisaj (\AquaHi) and BevatI 
it Piscium). They could also calculate the dhruvaka and 
viksepa of a star during the moment of its transit over the 
meridian of the place of observation. They calculated the 
daiama lagna ("known as the tenth house in astrological 
parlour) for the moment of transit from tables already 
constructed for the latitude of the observer, and this daiama 
lagna was the required dhruvaka of the star. By using 
two big vertical poles (i.e., gnomons) situated in the north- 
south line, the zenith distance of the star at transit could 
be determined from which the declination of the star was 
deduced, from the relation : 

Declination = latitude of place minus zenith distance. 

Since Viksepa (BS) = QS-QB i.e., declination of the 
star minus declination of a point B on the ecliptic [which 
is sin- x (sin I sin «)], the polar longitude (dhruvaka) and the 
declination give the viksepa which is thus : 
S — sin'^sin I sin «) 

Anyhow the above analysis seems to show that the 
co-ordinates of stars were determined at different epochs. 
Firstly when T was respectively 22° 21' ahead of the 
present T , secondly when it was 20° 8' ahead, and 
thirdly when it was 19° 21 ' ahead. The epochs come out 
to be 340 A.D., 500 A.D., and 560 A.D., respectively. 
The first epoch is nearly 200 years from the time of 
Ptolemy, and if it is assumed that Hindu astronomers 
assumed Citra (Spica or < Virginia) to occupy the first point 

I 264 J 

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of Bibra, the epoch comes out to be 285 A.D., and the 
corresponding Vernal point 2° to the west of Ptolemy's. 

This analysis shows that the Indian astronomers had 
arrived at the idea that the equinoctial point should he 
properly located with reference to some standard stars and 
there were probably three attempts, one about 285 A.D., 
the next about 500 A.D., and the last one about 570 A.D. 
They had not accepted the first point given by Ptolemy or 
any western astronomer. 

The compiler (or compilers) of the S.S. was clearly 
unconscious of the precession of equinoxes, and while in his 
report, he made a selection of these data, he did not perceive 
that they were inconsistent with the idea of a fixed V.E, point. 

But he did not err on the fundamental point. He had 
clearly laid down that Mesadi, i.e., the first point of Aries 
from which the year was to be started was to be identified 
with the vernal equinoctial point. 

It is to be noticed that though the maker of the S.S. has 
absorbed many of the ideas from Greek astronomy including 
the use of technical terms like hora, liptikd, kendra, etc., he 
did not either blindly copy the Graeco -Chaldean data. From 
whichever source he might have got the ideas, he absorbed 
it correctly and made an attempt to fix up the actual V.K 
point, as required in Chaldean astronomy, otherwise his 
zero-point would have been coincident with Ptolemy's. 
We have shown that whatever the Hindu zero-point of the 
zodiac might be, it is not coincident with that of Ptolemy. 


Gnomon Measurements in the Aitareya Brahmaaa 

References to the observation of the solstice are found 
in very early literature as the following passage from the 
Aitareya Brdhmana shows : 

'They perform the Ekavimsa day, the Vi^uvan^ in the 
middle of the year : by this EkavimU day the gods raised 
up the sun towards the world of heaven (the highest region 
of the heavens, viz., the zenith). Eor this reason , this sun 
(as raised up) is (called) Ekavimsa, of this Ekavimsa sun 
(or the day), the ten days before are ordained for the 
hymns to be chanted during the day ; the ten days after 
are also ordained in the same way ; in the middle lies the' 
Ekavimsa established on both sides in the Viraj (a period 
of ten days). It is certainly established in the Virdj. 
Therefore he going between (the two periods of 10 days) 
over these worlds, does not waver.' 

'The gods were afraid of this Aditya (the sun) falling 
from this world of heaven (the highest place in the 
heavens) ; him with three worlds (diurnal circles) of heaven 
(in the heavens) from below they propped up ; the Stomas 
are the three worlds of heaven (diurnal circles in the 
heavens). They were also afraid of his falling away 
upward ; him with three worlds of heaven (diurnal circles 
in the heavens) from above they propped up ; the Stomas 
are the three worlds of heaven (diurnal circles in the 
heavens) indeed. Thus three below are the Saptadasas 
(seventeen), three above ; in the middle is the EkavifnSa 
on both sides supported by Svarasamans. Therefore he 
going between these Svarasamans over these worlds does 
not waver*. 

This obscure passage has been interpreted as follows 
by Prof. P.C. Sengupta in his Ancient Indian Chronology. 

The Vedic year-long sacrifices were begun in the earliest 
times on the day following the winter solstice. Hence the 
Visuvan which means the middle day of the year was the 
summer solstice day. The above passage shows that the 
sun was observed by the Vedic Hindus to remain stationary 
1 e., without any change in the merdian zenith distance 
for 21 days near the summer solstice. The argument was 
this that if the sun remained stationary for 21 days, he 
must have had 10 days of northerly motion, 10 days of 
southerly motion, and the middle (eleventh) day was 
certainly the day of the summer solstice ; hence the sun 
going over these worlds, in the interval between the two 
periods of 10 days on either side, did not waver'. Thus 
from a rough observation, the Vedic Hindus could find the 
real day of the summer or winter solstice. 

The next passage from the Aitareya Brahma\ia (not 
quoted) divides the Viraj of 10 days thus ; 10 = 6 + 1 + 3- 
the first 6 days were set apart for a Sadaha (six day-) period, 
followed by an atir&tra or extra day and then came the 
three days of the three Stomas or Svarasamans. \The 
atiratra days before and after the solstice day were 
respectively styled Abhijit and Visvajit days. It may thus 
be inferred that the Vedic Hindus by more accurate 
observation found later on that the sun remained stationary 
at the summer solstice for 7 and not 21 days. 

Question may now be asked how could they observe fchat 
the sun remained stationary for 21 days and not for 
23, 27, 29, or 31 days. This depended on the degree of 
accuracy of observation possible for the Vedic Hindus by 
their methods of measurement. They probably observed 
the noon-shadow of a vertical pole. 


Precession of the Equinoxes amongst 
Indian Astronomers 

On p. 226, we have given references to pre-Siddhantic 
notices of the location of the vernal point in the sky. We 
saw that ancient Indian savants noticed its gradual shift 
( due to precession ), but were only puzzled by the pheno- 
menon. Let us see what was the experience of the 
Siddhantic astronomers in this respect. 

Dlksit, in his Bharatiya Jyolisastra, has summarized the- 
adventures of the idea of Preeession of the Equinoxes 
amongst Indian astronomers of the Siddhanta period. The 
following account draws heavily on his Chap. 3 ( p. 326 ) on 
Ai/ana-Calana, which literally means 'the movement of the 
solstitial points'. * 

The 'Solstitial points' were known amongst Indians as 
'Ayanas' anth Siddhantic astronomers regarded them as 
'imaginary planets' as they used to do in the case of the 
nodes of the lunar orbit. Though the nomenclature is cum- 
brous, the chapter actually deals with the precession of 
the equinoxes, as this point is 90° behind the summer 
solstitial point. 

Before the Siddhantic period, the lunar calendar was of 
primary importance, hence the exact fixation of the vernal 
equinoctial point ( T Q ) was not very important. It became 
important from the time the Indian astronomers of the 
Siddhanta period first realized that T Q should form the 
zero-point of the zodiac ; and made attempts at different 
epochs ( 285 A.D.-600 A.D. ) to give co-ordinates of stars 
(Dhruvaka and Vik$epa) with respect to this as the initial 
point. Chapter VIII of modern SUrya- Siddhanta gijves a 
resume' of these co-ordinates for, the junction-stars of the 
lunar asterisms. Our analysis of these data as given in 
Appendix 5-B shows that these co-ordinates must have 
been obtained by actual observations at different epochs, and 
as the compiler of the SUry a- Siddhanta was ignorant of the 
phenomenon of precession of the equinoxes, he made an 
uncritical selection of these data compiled at different times 
and included them in his Chap. VIII. 

From these data, it is impossible to determine the exact 
location of T at the time when the SUry a- Siddhanta was 
complied. So the wordy warfare between the upholders of 
the Citra-pak$a and the Bevati-pak$a becomes meaningless 
as pointed out on p. 262. 

* The word l Ayana Galana* strictly means the movement of the 
"Solstitial Points". Bhaskaracarya uses the word 'Sampat-Galcma' 
for movement of the equinoctial points ( T and £t ). Mathematically 
the two denominations are equivalent, but it has become the practice 
in Hindu astronomy to render the term 'Precession of the Equinoxes' 
by the words 'Ayana Calana*. We shall follow this practice through- 

The surmise that the early Siddhantic astronomers were 
ignorant of the movement of the equinoxes is supported by 
the fact that neither of the early eminent astronomers 
Aryabhata I (476 — 523 A.D.) nor Lalla (748 A.D.) whose 
dates are known, mention anything about precession of the 
equinoxes in their writings which have come down to us. 
If they derived their knowledge of astronomy from the West, 
they followed the current western practice of ignoring the 
precession. The astronomer Varahamihira, who wrote 
about 550 A. D., and has left us a compendium of the five 
Siidhantas, makes no mention of the phenomenon. This 
proves that the original SUrya SiddhSmta as known to 
Varahamihira contained no reference" to the movement of 
the equinoctial points. In his Bfhat SaUhita as mentioned 
on p. 226, Varahamihira, however, noted that the solstices 
were receding back, but he could not say anything about the 
actual nature of the precession or assign any rate to it. 

But it is obvious that once the Indian astronomers 
recognized T as the starting point of the zodiac, and started 
giving co-ordinates of stars in terms of T Q as the starting 
point, they could not avoid noticing the movement of the 
equinoxes, just as it happened with Hipparchos in Greece. 
According to Brahmagupta (628 A.D.), the first astronomer 
who made a pointed reference to it was one Visnu Candra 
author of the Vasitfha Siddhanta whose date is given as' 
ca. 578 A.D. He was supported by one &isena of whom 
only the name survives. For holding these views these 
astronomers were roundly abused by Brahmagupta whose 
views on these points appear to have been confused. But 
undeterred by the great prestige of Brahmagupta, later 
astronomers continued to make references to the movement 
of the equinoctial points. 

We cite some examples. 

MuSjala Bhata, a south Indian astronomer, wrote a 
treatise called Laghumanasa in 854 $aka or 932 A.D. A 
later commentator, Munisvara, ascribes the following 
verses to him. 

Uttarato yamyadisam yamyantattadanu 

parisaratam gaganasadam calanam kincid bhave- 

dapame. 1. 

Visuvadapakramamandala-sampate praci mesadih 
pascattula^iranayo-rapakramasambhavat proktafc. 2. 
Basitrayantaresmat karkadiranukramanmrgadisca 
tatra ca parama krantirjinabhagamitatha tatraiva. 3 
NirdiB^o-yanasandhiscalanam tatraiva sambhavati 
tadbhaganab kalpe syu-go-rasa-rasago-'nka-candra 

mitatu 4. 

C.R.— 42 



REPORT of the oalendab reform committee 


1. While the celestial bodies move in the sky from 
north to south and again from south to north, a very small 
variation takes place in their declination. 

2. The (ascending) node in which the celestial equator 
and the ecliptic intersect is the first point of Aries (Me§idi\ 
and it gives the 'East'. The second node is the first point 
of Libra (Tuladi), and these two points never change their 
-declination value (which is zero). 

3. The first point of Cancer (KarkZdi) is at a distance 
oi three signs (i.e. 90°) from it, and at a distance of three 
signs in the reverse order is the position of the first point of 
Capricorn (Makaradi), These give the positions of maximum 
declination which is 24 degrees. 

4. The solstitial points (which mark the ayanas) show 
a movement, and the number of their revolutions in a Kalpa 
is counted as 199669. 

The last passage recognizes processional motion, says 
that it is continuous, and gives^the rate as 59".9 per year. 
Munjala Bhata makes no mention of trepidation. He noticed 
that the Ayanas had processed by about 6° from the position 
given in the Surya-Sidtlh&nta. 

Prthudaka Svami (born 928 A.D.), an astronomer who 
observed at Peihowa, near Kuruksetra, commenting on a 
passage of Brahmagupta says : 

"The revolution of Ay ana in one Kalpa is 189411. 
This is called the Ayana Yugd". 
This passage recognizes the continuous nature of 
precessional motion, and gives the rate of processional 
motion as 56".82 seconds per year. 

So far we have no mention of the 'Theory of Trepidation' 
This is first mentioned in the Arya Siddhanta t ascribed to 
Aryabhata II, whose date is 1028 A.D. It says : 
Ayanagrahadot krantijyacapam kendravat dhanarnam syat 
Ayanalavastat samskrta khetadayana carapamalagnani. 12. 

Translation : — Find the sine declination {krantijya) of 
the ayanagraha (in a way similar to that of the sun's 
declination) ; from it deduce the amount of declination, 
plus (north) or minus (south), which is the amount of 
ayanafnsa* After applying this ayanafn§a-corToction to 
the planet, the values of cava (half the difference between 
the lengths of day and night), declination of planets, lagna 
(the orient ecliptic point), etc., are to be calculated. 

This has been interpreted as follows (Dlkgit, p.330). 

The equinox oscillates between ±24°, and the number of 
revolutions of the Ayana-pl&Tiet in a Kalpa is 578159, which 
gives the period of revolution as 7472 years and the annual 
rate of motion as 173 "A. During a quarter period viz,, 1868 
years, the ayanafn§a increases from 0° to 24°, at first, 
rapidly, then gradually more slowly like the increase of 

* This is a technical term used by Indian astronomers to denote 
the distance of the vernal point from the fixed Hindu Zodiac, 

declination of the sun. Thereafter it diminishes in like 
manner and after the lapse of 3736 years, i.e. the half period, 
it again becomes zero and goes on the other side. The annual 
rate of motion, which on the average amounts to 46 .3 
seconds, varies fromzfc 70"*5 to ' 

We now come to a very controversial passage in the 
modern SUrya Siddkcinta, Chap. Ill, verses 9 to 12. 
These are : 

Trimsat krtyo yuge bhanarii cakrarii prak parilamvate 
tadgunad bhudinairbhaktat dyuganat yadabapyate. 9 
Taddostrighna dasaptamsa vijtieya ayanabhidhat 
tatsamskrtadgrahat kranticohaya caradaiadikam 
sphutam drktulyatam gacchedayane visuvadvaye. 10 
Prak cakram calitam hine chayarkat karanagate 
antaramsai rathavrtya pascacchesaistathadhike. 11 
Evaih visuvaticchaya svadese ya dinardhaja 
dak^inottara rekhayaih sa tatra visuvat prabha. 12 

9. In an Age [yuga\ the circle of the asterisms (bha) 
falls back eastward thirty score of revolutions. Of the 
result obtained after multiplying the sum of days (dyugatya) 
by this number, and dividing by the number of natural 
days in an Age, 

10. Take the part which determines the sine, multiply 
it by three, and divide by ten ; thus are found the degrees 
called those of the precession (ayana). From the longitude 
of a planet as corrected by these are to be calculated the 
declination, shadow, ascensional difference (caradala) etc. 

11. The circle, as thus corrected, accords with its ob- 
served place at the solstice (ayana) and at either equinox ; it 
has moved eastward, when the longitude of the sun, as obtain- 
ed by calculation, is less than that derived from the shadow. 

12. By the number of degrees of the difference ; then, 
turning back, it has moved westward by the amount of 
difference, when calculated longitude is greater. 

These verses occur in the chapter on astronomical 
measurements by the gnomon, and are misfits there ; 
according to all authorities, these verses did not exist in the 
original SUrya-Siddhanta, but have been extrapolated there, 
and have no reference to the context of the chapter. The 
extrapolation must, however, have taken place before the 
time of Bhaskaracarya II (1114-1178 A.D.), because he 
comments on this passage. 

The passage supports the theory of trepidation and says 
that the amplitude of precessional oscillation is 27° and the 
period of one complete oscillation is stated to be 7200 years. 
The rate of precession is given as 54" per year, which is 
uniform and the same throughout the oscillation. These 
stanzas are quoted by Indian astrologers who are advocates 
of the nirayana system, in support of their arguments for 
sticking to the sidereal year. They say that the present 
ayanafnia is about 22°, and T will go on processing for 
another 350 years till ayan&?ri§a becomes 27° and will" then, 
turn back on its return journey. 



This is sufficient argument to them to turn down all 
proposals lor S&yana reckoning taking the length of the 
year to be tropical. 

We now take the opinion of the last great Indian 
astronomer Bhaskaracarya II (1150 A.D.). 

He uses the term * Sampat-Calana* i.e., movement of the 
intersection of the ecliptic and the equator, instead of the 
classical term Ayana. He says : 

Siddhanta &iromani f Goladliyaya, 
Golabandhadfii k&ra 

Tasya [visuvatkrantivalayapatasya] api calanamasti. 
Ye'ayanacalana bhagah prasiddhasta eva vilomagasya 

krantipatasya bhagah 

TranslatiXm : — It (the equinox) has also movement. 
What is commonly known as the amount of precession 
(ayanafn&a) is the same as the longitude of the equinoctial 
point measured backwards. 

This evidently shows that he regarded the change as due 
to the retrograde motion of the node (i.e. equinoctial point) 
like modern European astronomers. 

He criticises Brahmagupta for his views on Ayana 
Calana and says : "One can observe that at the time of 
Brahmagupta, the ayanain&a value was very small and 
hence it is likely that it could not have come to his notice ; 
yet how is it that he did not take the rate of revolution of 
equinoxes as given by the Sury a- Siddhanta, just as he has 
taken figures for rates in some other cases on the basis (or 
authority) of already proved and accepted rates". 

He further says : 

Ayanacalanam yaduktam Munjaladyaib sa evayam 


tatpakse tadbhaganafr kalpe go'ngartu-nanda-go-candrah 


Atha ca ye va te va bhaganah bhavantu yada ye'msa 
nipunairupa labhyante tada sa eva krantipatab- 

Translation : — "What Munjala and others have mention- 
ed as Ayana Calana 1 ', is nothing but the motion of this 
equinoctial point. According to their view the number of 
revolution in a Kalpa is 199669 (yielding annul rate of 
59".9). Let whatsoever be the number of revolutions, 
whatever amount is obtained by expert observers is the 
angle of precession for that time." 

From this it is clear that he recommends one to accept 
the ayanafnia which one would actually get by observation 
of sun's place at any particular time. Dlksit says : 

I have not come across single statement in which 
Bhaskaracarya has clearly said that equinoctial point makes 
a complete "circular revolution", nor does be say that "it 
does not make it". 

He has taken 1 minute per year as the ayana-motion 
and has supposed 11° as th« ayandlh&a in l^aka 1105. He 
thus means to take Saka 445 as the zero-precession year. 

We thus perceive that Indian astronomers up to the time 
of Bhaskaracarya were as much divided in their ideas about 
precesssion of the equinoxes as the contemporary Arab 
astronomers of the West (Hispano- Muslim), and the East. 
It is only after 1024 A.D. that they adopted a theory of 
trepidation. The earlier-astronomers like Munjala and 
Prthudaka merely noticed precession and gave their own 
rates for it. Bhaskaracarya is non-committal about 
trepidation. The Indian astronomers do not appear to have 
been influenced by the views of the western astronomers, 
the earlier Greeks or later Arabs. 

It will be sheer stupidity to hold to the theory of 
trepidation of equinoxes 270 years after it has been definitely* 
proved to be wrong. The law of universal gravitation will 
not be changed by God Almighty to oblige astrologers. 


The Jovian Years 

{Barhaspatya Var§a) 

The sidereal period of Jupiter, according to the SUrya 
Siddhanta is 4332.32 days which is nearly 11.86 sidereal 
years. Therefore Jupiter roughly stays for one year in one 
zodiacal sign, if we calculate by mean motion. 

This was taken advantage of to devise a cycle of 12 
Jovian years. If we divide the Sury a- Siddhanta period by 
12, we get 361.026721 days which is taken as the length of 
a Jovian year. This is 4.232 days Ie3s than the Surya 
Siddhanta solar year. So if a Jovian year and an ordinary 
solar year begin on the same day, the Jovian year will 
begin to fall back, completing a complete retrogression 

in 85 — solar years, according to the SUrya- Siddhanta. 

So 85— solar years — 86^^ Jovian years, and one Jovian 
2i 1 1 All 


year is expunged in every 85^[ years. The expunged year 

is called the Kmya year. In actual practice, the interval 
between two expunctions is sometimes 85 and sometimes 
86 years. 

There was indeed at one time a period of 12 Jovian 
years, but at some past epoch, a fivefold multiple, a cycle of 
60 Jovian years, each with a special name suffixed by the 
word 'Saihvatsara', came into use. 

The beginning of the Jovian years is determined by the 
entry of Jupiter into an Indian sign by mean motion, the 
1st, 13th, 25th, 37th and 49th years 'being marked by the 
entry of Jupiter into the sign Kumbha, and not Mesa which 
is otherwise the first of the signs of the Siddhantas. It 
thus appears that the system of counting Jovian years is a 
pre-Siddhilntic practice 

The sixty-year cycle is at present'in daily use in Southern 
India (south of Narmada) where each year (the solar year or 
the luni-solar year) is named after that of the corresponding 
Jovian year. The years are counted there in regular succes- 
sion and no safnvatsara is expunged. This practice is being 
followed since about 905-06 A.D. (827 Saka), as a result of 
which the number of Northtlndian Safnvatsara has been 
gradually gaining over that of the South from that time. 
The Saka year 1876 (1954-55 A.D.) is named 41 Plavanga 
in the North while in the South it is 28 Jaya. 

The following are the names of the different years ; 



(21) Sarvajit 

(41) Plavanga 



(22) Sarvadharin (42) Kilaka 



(23) Virodhin 

(43) Saumya 



(24) Vikrta 

(44) Sadharana 



(25) Khara 

(45) Virodhakrfc 



(26) Nandana 

(46) Paridhavin 



(27) Vijaya 

(47) Pramadin 



(28) Jaya 

(48) Ananda 



(29) Manmatha 

(49) Kuksasa 



(30) Durmukha 

(50) Anala (Nala) 



(31) Hemalamba 

(51) Pingala 



(32) Yilamba 

(52) Kalayukfca 



(33) Vikarin 

(53) Siddharthin 



(34) ^arvarl 

(54) Eaudra 



(35) Plava 

(55) Durmati 



(36) Subhakrt 

(56) Dundubhi 



(37) ^obhana 

(57) Rudhirodgarin 



(38) Krodhin 

(58) Baktaksa 



(39) Visvavasu 

(59) Krodhana 



(40) Parabhava 

(60) Ksaya (Aksaya) 


Achelia, Elisabeth (1955)-— Of Time and the Calendar, 
New York. 

Alter, D. & Cleminshaw, C. H. (1952)— Pictorial Astronomy, 
New Yotk. 

Aryabhatiya of Aryabhata — translated with notes by 

W. E. Clark, Chicago, 1930. 
American Ephemeris it Nautical Almanac for the years 

1954 and 1955. 

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Abbe Mastrofini, 171 

Abd al-Rahaman al-Ruff, 206 

Achelis, Miss Elisabeth, 12, 171 

Adar, 179 

Addaru, 175,176 

Adhika ( = mala) month, 7, 247, 230 
Agni, 210 

Ahargana, 9, 11, 101, 102, 163 
Ahoratra, 157, 100 

Aitarcya BrTihmana, |89, 216, 219, 22], 266 
Akber, 1,159, 214, 251 
Aksaya ti tiya, 18, 39 
Al-BattanT, 204, 200, 240 ; 

rate of precession, 206 
Alberuni,198,204, 237-; 
Al-Bitruji, 206 

Alexander of Macedon, 202, 213, 234, 235 

Al-Fargham, 206 

Almagest, 204, 206, 238, 240 

Aloysius LiliuB, 171 

Altekar, Prof., 254 

Al-Zarquali, 206 

Amanta month, 101, 157, 177, 247 
Ammonia clock, 32, 159 
Anaximander of Miletus, 188, 202 ; 

gnomon. 202 
Ancient Indian Chronology, 215, 253,-266 
Andan (inscription), 233 
Antiochus Sorter, 203 
Antiochus I, II of Babylon, 228 
Anubis, Egyptian god, 164 
Anuvatsara, 225 

Anyanka Bhlma Deva of Ganga dynasty, 257 

Aparabna, 108 

Jpastamba Samhita, 218 

Aphelion, 242 ; movement of, 243 

Apolloniu s of Perga, 203 

Ara (inscription), 230 

Arachosia, 229, 230 
Aranyaka, 214 
Archebius of Taxi la, 230 
Archimedes of Syracuse, 203 
Archytas of Tare n turn, 202 
Ardeshir I of Persia, 232 
Ardharatrika system, 1, 253,^254 
Ariana, Herat regions, 229 
Aries (zodiacal sign), 392, 193 
Aries, first, point uf , 157, 192, 199, 207, 239, 240, 
262, 268 ; 

Hipparcho's, 200, 205, 206 ; 

movement of 200, 205, 206 ■ 

position in different times, 200 (fig). 

Ptolemy's, 200 
Aristaivhos nf Samos, 203 
Armellini, 171 

Armillary sphere, 199 (fig.), 263 
Arsaces of Parthia, 178 
Artabanus I of Parthia, 213 
Artabanus II of Parthia, 256 

Artemidorus of Puskalavati, 230 
ArthakUstra of Kautilya, 235, 236 
Aruiiodaya, 108 

Aryabhata 1, 204, 234, 236, 237, 238, 240, 2c 

253, 254, 267 
Aryabhata II, 238, 268 
Iryabhatlya of Aryabhata, 162 238, 253 
Arya Saiigamika, 232 
Irya Siddhanta, 1, 214, 251, 268 
Arya Vasula, 232 
Asokachalla Deva, 256 
Asoke, 177, 212, 227, 228, 252 
Assouan papyri, 179 
Jjitadhyayl, 214 
Astrolatry, 235, 236 

Astrology, 12. 194, 196, 205, 206, 235, 236, 256 
Atharva Sathhita, 217, 218 
At harm Veda, 214, 217, 218 
Audayika system, 254 

August Gompte, French positivist philosopher 

Augustus, 168 

Ayanamsa, 5, 7, 16, 17, 20, 268, 269 ; 

amount of acc. to Aryabhata II, 268 

amount of fixed, 16, 17 

(see also calendar for five years) 

definition, 268 

rate of, 7 

rate of Bhaskaracarya, 269 

value of, 7, 17 
Ayanas, 267. 268, 269 
Azes, 256 

Azes I, 230, 233, 256 
Azes II, 230, 233, 256 
Azilises, 230, 233 

Babylon, 225, 226, 228 ; latitude of, 225 
Bachhofer, Dr. L., 230, 231, 232 
Badami (inscription), 233, 253 
Bailey, 253 
Balarama, 227 
Banerjce, late R. D,, 212 
Bentley, 253 

BeroHsus, Chaldean priest, 203 
Bharatiya JyotilQstra, 11, 160, 219, 225, 236, 

Bhaskaracarya, 238, 246, 262, 267, 268, 269 ; 

a van a calana, 269 
BkCtsmtl 160 
Bhattotpala, 237 
Bhoga (celestial longitude), 262 
Bija (correction), 3 
Box lid (inscription), 230 
Brahma. Creator in Hindu mythology, 223, 

236,238, 239, 240 
Brahmagupta, 223, 237, 238, 240, 253, 267, 268, 


Brahma Siddhanta, 1, 214 

Brahmanas, 193, 214, 221, 241, 245 
Brahrm, 227, 229, 231, 232, 233 
Brhat Samhita, 226, 267 
!, Brown, 193 

Buddha, 231,235; 

nirvana of, 256, 257 
views on astrology. 235 
Budhagupta, Gupta emperor, 234 
Burgess, Rev. E., 238, 253, 262, 263 

Calendar, defined, 1, 157 ; 
civil, 6 , 

compilation according to S. S., 1 ; 
confusion in Indian, 10 ; 
Egyptian, 164 ; 
French revolution, 167 ; 
Fusli, 248 ; 

Gregorian, 1, 3, 11, 170-172 ; 
Hejira, 1, 166, 179, 180, 214; 
history of reform movement, 10, 11 ; 
Iranian (Jelali) 1, 166 167 ; 
Islamic, 179, 180 ; 
Jewish 179 ; 
lunar, 3,179, 245,247 ; 
luni solar, 1, 3, 174, 249, 251 ; * 
calendar in Siddhantas 245-251 ; 
of Babylonians, Macedonians, Roma* 

and the Jews, 176, 177 ; 
principles of 174 ; 
Siddhantie rules for 247 ; 
National, 12-14 ; 
Paitamaha Siddhanta, 223, ; 
problems of the, 158, 159 ; 
Reformed, 4 ; 
Religious 7 ; 
Roman, 168 ; 

Seleucid Babylonian, 229 ; 
Siddhanta Jyotisa period, 245, 246 
Solar, 1,2, 164-173, 245; 

Siddhanta Jyotisa period, 234-245 
Tarikh-i-Jelali, 166, 167 ; 
Tarikh-Ilahi, 1, 214, 251, 257, 258 ; 
Vedanga Jyotisa, 9, 221, 222, 223 ; 
World, 1, 171-173 
Calendar of India, Reformed (as recommended 
by the Committee), 41-100 ; 
explanation of terms used, 40 
Calendar Reform, 

suggestion received, 5 ; 
summary of suggestions, 32-38 
Calikya Vallabhesvara, 233 
Caliph Omar, 167, 179 
Calippos, length of season, 175, 261 
Canakya, 213, 235, 236 
Cancer, first point of, 192, 199 
Candragupta, Maurya, 213, 236, 257 
Candragupta II, Vikramiiditya, 254, 255 
Capricorn, first point of, 192 



Cara , correction , 268 
Cardinal days, 189 
Cardinal points, 189, 190, 219; 

determination of, 190 
Castana, 6aka Satrap, 233, 256 
Centauries. 163 

Central Station, 3, 4, 7, 14, 40 
Chadwick, 202 

Chaldean Saras, 184,135, 186,202 
Christ, Jesus, 157, 201 
Chronometer, 157 
Cicero, 205 

Cleostratos of Tenedos, 193, 202 ; 

zodiac, 193. 202 ; 

8-year cycle of intercalation, 202 
Clepsydra, 159, 223, 225 
Committee, Indian Calendar Reform— 

appointment of, 4 ; 

dissenting note, 8, 18 ; 

final recommendations of civil, 6, 7 ; 

final recoromandations of religious, 7, 8 ; 

members of, 4 ; 

proceedings of the first meeting, 9 ; 
proceedings of the second meeting, 15 ; 
proceedings of the third meeting, 17 ; 
terms of reference. 4 
Committee, Indian Ephemeris and Nautical 
Almanac, 8 

Committee meetings, 4, 5 ; resolutions of 4, o 
Compline (division of day), 159 
Constantine, Roman emperor, 170 
Co-ordinate, celestial, Siddhantic designation 
of, 262 

Copernicus, 195, 203, 206, 235 
Corpus'lnscriptionum Indicantm, 229 
Ctujamani yoga, 108 
Cunningham, 230, 231 
Cycle of Indiction, 162 

Dak?inayana, 189. 219, 226, 239, 260 
Panda ( = n&4i or ghatika), 160 
Darius I, Achemenid emperor, 166, 176, 212, 


apparent length of, 226 ; 
astronomical, 159 ; 
civil, 159 ; 
counting of the 

succession of, 248 ; 
definition of, 157, 217 ; 
designation in ancient 

time, 183 ; 
division among Egyptians, 160 ; 
division among Hindus, 160 ; 
Julian, 161, 162 ; 
length of, 157, 159,259; 
length at Babylon, 226 ; 
length of longest and shortest, 225 ; 
mean solar, 157, 158, 159,197 ; 
reckoning of 13, 14 ; 
saura, 197 ; 
sidereal, 157, 158 ; 
solar. 157 ; 
starting of, 1 ( 5, 7 ; 
sub-divisions of, 159 ; 
Debevoise, 230 


Decad, 164 
D' Eglantine, 167 
Declination, 192, 204, 263 

Demetrius, 213 
Democritos of Abdera, 202 
I?ewai (inscription), 229 
Dkarma Sindhu, 19, 101 
Dhruva (celestial pole), 190, 192 
Dhruvaka (polar long.), 192, 262, 263, 267 

of junction stars, 264, 265 
Dlgha NikZya, 235 

Diksit, S. B., 11, r9, 160, 212, 219, 223, 224, 225, 

Diopter, 203 

Dios, Macedonian month, 179, 229, 255 
Direct motion, 169, 195 
Discovery, 190 
DurgastamT, 108 
Dvadasaha, 217 

equatorial axis of, 208 ; 
period of rotation, 12 ; 
polar axis of, 208 ; * 
speed in a second, 195 *, 
spinning of, 208 
Easter, 170, 171 
condition of, 185 ; 
list of lunar, 186 ; 
list of solar, 187 ; 
periodicity of, 185 ; 
recurrence of, 186 ; 
saros cycle, 184-187 ; 
Ecliptic, 158, 181. 191, 192, 197, 198, 207, 259; 
definition of, 191 ; 
earliest mention of, 199 ; 
fixing of, 191 ; 
plane Of, 192,207; 
pole of, 192,208; 
obliquity of, 191,207, 208,225 
Ekadasi, observance of, 105 
Elements of Euclid, 202 
Elliptic theory, 243 

Encyclopaedia Britannica, 170, 179, 199 
Epagomenai, 164 
Ephemerides, 201 
Ephemerides Committee, 4, 6 
Epicycle, 203 
Epigehis, 165 

Epiqraphia Indica, 233, 254 
Equator, celestial, Ml, 192, 197, 207, 239, 259 
Equinoctial days, 188 
Equinoxes, 188 ; 

autumnal, 189, 192 ; 

oscillation of, 268 ; 

vernal, 2, 11, 13, 188, 189,192, 205, 253, 

Era, 13, 177, 228-231, 236, 251, 252, 258 ; 
Amli,244,257,258 ; 
Arsacid, 178,230; 
Bengali San, 257, 258; 
Buddha Nirvana, 256-258 ; 
Burmese, 162 ; 
Cfclukya Vikrama^258 ; 

Era — eoHtd* 

Christian, 170, 251, 258; 

current, 251 ; 
Diocletion, 162 ; 
elapsed, 251 ; 
French Revolution, 167 ; 
Gupta, 255, 257,258; 
Harsa, 254, 258; 
Hojira, 162,180, 258; 
introduction of, 177 ; 
Jelali (Iranian), 162 ; 
Jewish era of Creation, 179 ; 
Jezdegerd (Persian), 162 ; 
Kalachuri (Chedi), 234 ; 
Kaliyuga, 13, 162, 252, 254, 258 ; 
Kanaka, 232, 256 ; 
Kollam, 257, 258 ; 
Kollam Andu, 257 ; 
Krta, 254 ; 
Kusana.231,232 ; 

inscription of, 230 ; 
method of date-recording, 232 ; 
Laksmana Sena, 258 ; 
Laukika kala, 258 ; 
Maccabaean, 179 ; 
Magi, 258 ; 

Mahavira Nirvana, 258 ; 
Malavagana, 254 ; 
Nabonassar, 162, 177, 178, 253 ; 
Newar, 162, 258 ; 

Old 6aka, 230, 232-234, 236, 255, 256 ; 
Olympiads, 178 ; 
Pan«Java kala, 252 ; 
Parasurama, 257 ; 
Parganati Abda, 257 ; 
Parthian, 178, 256 ; 
Philippi, 162 ; 
Raja 6aka, 258 ; 

6aka,2,4,6, 13, 162, 178, 214, 233,234, 
236, 255-258 ; earliest records of, 233 ; 
Saptar^i, 190, 252, 258 ; 
Seleucidean, 161, 176, 178, 179, 229, 230, 

231, 255, 256 ; 
Vallabhi, 258 ; 

Vikrama, 13, 234, 247, 254, 255. 257, 258 ; 
Vilayati,244, 257,258; 
Yudhist-Mra, 252, 258 
Eratosthenes, 178 ; on diameter of the earth, 

Euclid, 202, 203 
Eucratidas, 229 

Euctemon, length of season, 175, 261 
Eudoxus of Cnidus, 201, 202 ; on geometry , 203 
Euphrates, river, 157 
Euthydemids, 213 

Exact Sciences in Antiquity, 3, 197, 198, 201 

Fabricious, 235 

Fatehjang (inscription), 229 

Festivals, Religious- 
Alphabetical list of, 111-115 
Christian, 126 ; 
general rules for, 101 ; 

ft H — 43 



festivals, Religious— eontd. 

Lunar—general rules for, 102-105 ; 

dates of, 119-124 
Moslem, 125; 

Solar— general rules for, 106 ; 

dates of, 117-118 ; 
South Indian— general rules for 106 ; 
Fotheringham, Dr. J. K., 165 

Galilio, 159 

Gandhara, 225, 226, 229, 230 ; latitude of 225 
Ganesa caturthT, 108 
Oanges, river, 157 
Gangooly.P. L.,238 
Garga, 226 ; receding of solstices, 226 
Garga Samkita, 226 
Gargasrota, river, 226 
Gauna (mana), 247, 248 
Geminus, 197 
General Astronomy, 158 
Geocentric theory, 204, 239 
George Washington, birthday of, 161 
Gesh (division of time), 160 
Ghatika, 160 
Ghirshmnn ) 232 
Ginzel, F. K. 162, 193 

Gnomon, 159, 174, 188, 189, 202, 219, 223, 268 ; 

measure meat in Aitareya Brahman a, 266 
Gondophernes, 178, 230 
Gorpiaios, Greek month, 231 
Great Hear (Sap tarsi), 190 
Greek Olympiads, 178 
Greenwich time (U. T.), 14 
Gregory XIII, Pope, 2, 10, 11, 170, 171 
Gunda (inscription), 234 
Guptas, 254, 255, 257 

Hajj, 180 

Hammurabi, Babylonian king, 175 

Harappa, 212 

Harsa Vardhana, 254 

Hashim, Amir AH, 180 

Haug, Dr. Martin, 216 

Heliacal rising, 164, 191 

Heliocentric theory, 203 

Herzf eld, 232, 255 

Heeiod, 201 

Hidda (inscription), 230 

Hipparchos of Nicaea, 165, 166, 177, 178, 192, 
197, 200, 201, 203, 205, 206, 226, 235, 
•237, 240 ; 

catalogue of stars, 203 ; 
discovery of precession, 205, 267 ; 
first point of Aries, 200, 205, 206 ; 
geometry & spherical trigonometry, 203, 

Hippocrates of Chios, 202 
History of Science , 206 
Hoang Ho, river, 157 
Holidays, 5, 6 ; list of, 117-154 ; 

Ajmer, 145 ; 

Assam, 128 ; 


Bihar, 129 ; 

Bilaspur, 147 ; 

Holidays, list of — contd. 
Bombay, 130 ; 
Christian festivals, 126 ; 
Coorg, 148 ; 
Delhi, 149 ; 
East Punjab, 134 ; 

Fixed holidays & solar festivals, 117, 118 ; 

Govt, of India, 127 ; 

Himachal Pradesh, 150 ; 

Hyderabad, 137 ; 

Jammu & Kashmir, 138 ; 

Kutch, 151 ; 

Lunar festivals, 119-124 ; 
Madhya Bharat, 139 ; 
Madhya Pradesh, 131 ; 
Madras, 132 ; 
Manipur, 152 ; 
Moslem festivals, 125 ; 
Mysore, 140 ; 
Orissa, 133 ; 

Patiala & East Panjab States Union, 141 ; 

Kajasthan, 142 ; 

Saurashtra, 143 ; 

Travancore-Cochin, 144 ; 

Tripura, 153 ; 

Uttar Pradesh, 135 ; 

Vindhya Pradesh, 154 ; 

West Bengal, 136 
Hora, 236, 266 
Horoscope, 196, 205, 256 
Horoscopic astrology, 194, 196, 204, 256 
Hour circle, 191 

Hsiu, Chinese lunar mansion, 182, 183, 210, 
211, 224 ; 

names with component stars, 210, 211 ; 

starting of, 183 
Huviska, 231 
Hypatia, 204 

Ibn Yunus, 206 
Idavataara, 225 
Ides, 168 
Idvatsara, 225 
Iliad, 201 

Indian Calendar ,246 
Indian Ephemeris, An, 101 
Indian Ephemeris and Nautical Almanac, 

5, 8, 12, 14, 17 
Indra, Indian god, 199, 215, 216 
Indus, river, 157 
Intercalary month ( = malamasa), 175, 176, 
245, 246j 

Babylonian calendar, 176 ; 

calculation of, 246, 249 ; 

definition of 247 ; 

eight-year cycle, 202 ; 

Islamic calendar, 180 ; 

Jewish calendar, 179 ; 

list of acc. to modern calculations, 250 ; 

list of according to S. S., 250 ; 

19-year cycle, 176, 200, 202, 229, 245, 246 ; 

Paitamaha Siddhanta, 223 ; 


Romaka Siddhanta, 237 ; 

Siddhanta Jyotisa, 246, 248 ; 

Vedanga Jyoliga, 223, 224, 225, 246 

Introduction to the History of Science, 159 
Isis, Egyptian god, 164, 165 

Jacobi, 215 

Jaikadeva, 254 

Jai Singh of Amber, 10 

Jamotika, 6aka king, 233 

JanmaHamI, 19 

Jatakas, 239 

Jayanti, names of, 107 

Jay as wall, 255 

Jehonika, 230 

Jelaluddin, Melik Shah, 166 
Johann Werner, 206 
Jones, Sir Harold Spencer, 6, 12, 158 
Jovian cycle, 257 

Jovian (Barhaspatya) years, 270 ; 

names of, 270 
Julian days. 161, 162 
Julian days of important events, 162, 163 
Julian period, 162 

.Julius Caesar, 2, 10, 159, 165, 168, 241 
Junction stars, of'naksatra, 184, 210, 211*. 900 ; 
262-265 ; 

dhruvaka of, 261, 205 ; 
latitude oi (1950), 220, 264, 265 ; 

(1956), 184, 210, 211 ; 
long, of (1956), 230, 264. 265 ; 

(1956), 184. 210. 211 ; 
magnitude of, 210, 211, 264, 265 
Jupiter, planet, 194, 195, 203, 239 ; 

sidereal period of. 270 
Jya (chord), 204 
Jyoti>a Karanda, 223 

Kabishak, 180 

Kadamba, pole of the ecliptic, 192 

Kala or liptika, 160 

Krdaloka Prakasa, 223 

Kalasang (inscription), 229 

KalastamT, 108 

Kaldarra (inscription), 229 

Kalends, 168 

Kalhana, Historian of Kashmir, 252 
Kali, 162 ; long, of planets at Kali beginning 

Kalidasa, 7, 261 

Kalpa, 162, 175, 214, 240, 268, 269 

Kalpadi, names of, 107 

Kandahar, 229 

Kaniska, 230, 231, 236, 256 

Kanaka I, 231 

Kaniska II, 232 

Kaniska III, 231, 232 

Kaniska Casket (inscription), 230 

Kaniza Dheri (inscription), 231 

Kanva, 213, 228 

Kapisthala Ka^ha Samhita, 218 
Kapsa, 230 
Karana, 163 

Karanas, definition, names and calculation of, 

110 ; lords of, 110 
Kanaka, 218 

Kaurpa (name of a sign), 193 



Kautllja, views on astrology, 236 
Keith, Or. Berriedale, 218 
Kendra, 236. 266 
Kepler, 2, 206, 242 
Ketu (node), 186 
Kbalatse (inscription), 229 
Khav4akhadyaka of Brahmagupta, 162. 240- 

Kharorthi (inscription), 229, 230, 231, 233 
Khotani 6a ka (language), 231 
Kidinnu, 200 

Konow, Dr. Sten, 229, 231, 255 
Kranti (declination), 262 
Krttikas, 182, 219, 252 
Ksaya month, 247, 248 250 
Kugler, 176, 196, 225 
Kumbha mela, 6 
Kumbha yoga, 108 
Kurram (inscription), 230 
Kuruksetra, latitude of, 225 
KuSanas, 213, 230-234, 236, 252, 256 

Lagadha, 214, 222 

Laghumanasa of Mnnjala, 162, 267 

Lagna (orient ecliptic point), 237, 268 

Lagrange, 167 

Lalla, on precession 267 

Lambaka (co-latitude), 239 

Lanka. Greenwich of ancient India, 239, 253 

Laplace, 167 

Latitude, celestial, 192,203, 204, 210, 211, 264 

polar, 192, 263, 264, 265 
Leap year, 6, 13, 15 ; of Islamic calendar, 180 ; 

of Reformed Calendar of India, 186 
Leonardo of Pisa, 160 
Leeuw, Mrs. Van Lohuizen, 232, 255, 256 
libra, first point of, 192, 199, 239, 262, 268 
liptika, 160, 236, 263, 266 
Lockyer, Sir Norman, 190 
Lokambhaga of Simhasuri, 233 
Longitude, celestial, 7, 192, 203, 204, 210, 211 

253, 264, 265 ; 

polar, 192, 263, 264, 265 
Longitudes of planets at Kali-beginning, 253 
Ltiders, 228, 232 
Lunar eclipse, 185 
Lunar mansions, 182 ; 

of Rg Veda, 217 ; 

stars of, 210, 211 
Lunar year, beginning of, 220, 221 
Lunation, duration of, 158, 174, 175, 246 ; 

length of, 164, 248 

Madhyahna, 101, 108 

170, 183, 185,219, 221, 227, 228, 

239, 252 ; 

month reckoning in, 185 ; 

time of compilation, 226, 252 
Mahadvadasi, defined, 107 
Mahftyuga, 160, 162, 217, 254 
Maira (inscription), 229 
Maitrayanl Sarhhita, 218 
Mal&m&sa, 246, (see also intercalary month), 
Mamine Pherl (inscription), 231 

Miinikiala (inscription), 230 
M&nsehra (inscription), 229 
Manvadi, names of, 107 

Manzil, Arabian lunar mansion, 182, 183, 
210, 211 ; 

names with component stars, 210, 211 ; 

starting of, 183 
Marguz (inscription), 229 
Mars, planet, 194, 195, 203, 239 ; 

retrograde motion of, 194 
Masakrt, 174 
Matins, 159 
Maues, 230, 233 
Mauryas, 228 
Max Miiller, 183, 214, 215 
Maya, 236, 238 
Mean solar day, 157, 158 
Mean solar time, 158 
MeghadTda of Kalidasa, 261 
Melik Shah the Seljuk, 159 
Menander, 213, 229, 235 
Menelaos (Greek astronomer), 204 ; 

Spherical trigonometry, 204 
Mercedonius, 168 
Mercury, planet, 194, 195, 203, 239 
Meridian passage, 57 
Mesadi, 239 

Mesadi, sidereal, 16, 17, 40 
Meton of Athens, 176, 202 ; 

ninetcen-year cycle, 202 
Metonic cycle, 162, 176 
Milimla Panho (philosophical treatise), 229 
Mithra (Persian god), 167, 170 
Mithradates I, 213, 255 
Mithradates II, 213, 255 
Mitra, Indian god, 215 
Moga, £aka king, 230 
Mohammed Ajmal Khan, 180 
Mohammed, Prophet, 159, 179, 180 
Mohenjodaro, 212 
Moise of Khorene, 232 
Month, anomalistic, 197 ; 

beginning in Babylonian calendar, 185 ; 
definition of, 157, 158, 185 ; 
draconitic, 186, 197 ; 
intercalary {sec intercalary month) ; 
Lunar, 220, 221, 225, 245, 246 ; 

commencement of as recommended 

by the Committee, 7 ; 
names of Indian, Chaldean and 
Jewish, 177 ; Macedonian, 177, 229 ; 
length of Islamic, 180 ; 
interpretation of month names, 221 ; 
length acc. to S. S-, 246 
reckoning in Mahabharata, 185 ; 
relation between draconitic and synodic, 

sidereal, 223 ; 

Solar, causes of variation in length, 243 ; 
commencement of, 7 ; 
definition of, 242 ; 

different conventions in beginning 

of, 244; 
duration of, 243 *, 
Egyptian, 164 ; 
first month of the year, 5, 6 ; 

Month, Solar— contd, 

Iranian names, 166 ; 
length of, 211, 242-246, 251 , 
length recommended by the 

Committee 2, 5, 6, 13, 15 ; 
names in French Revolution 

calendar, 167 j 
names in Yajur-Veda, 218 ; 
names of, Indian 5, 6, 7, 14, 15 ; 
names, Persian 166, 167 ; 
number of days in Vedanga Jyotisa, 


variation in length, 1 
Synodic period, 197, 223 
Moon, crescent of, 182 ; . 

deviation of path from the ecliptic, 192, 

inclination of path to the ecliptic, 201 ; 

limiting values of true motion, 197 ; 

mean daily motion, 197 ; 

motion of, 182 ; 

movement of, 31, 181, 182 ; 

rate of motion over the sun, 184 ; 

sidereal period of, 182 ; 

synodic period of. 182 
Mount Banj (inscription), 229 
Mucai (inscription), 229 
Muhurta, 100, 108, 160 ; lords of, 109 
Mukhya man a, 247, 249 
Mtd Apin, Babylonian astrological text, 198 
Munievara, commentator, 267 
Munjala Bhata, 11, 259 

on precession, 267-269 
Mural quadrant, 203 

Nabu Nazir, 177 
Naburiannu, 200 
Nadir, 157 
Nagabha^a, 257 
Nahapana, 233 

Naksatra, average length of, 224 ; 
beginning of, 14, 229 ; 
calculation of (acc. to the recommenda- 
tions of the Committee), 5, 7, 16, 17 ; 
component stars of, 210, 21 1^ 
def. of in earliest times, 183. ,218, 227 
def. of in Vedanga Jyotisa, 183, 223-225 ; 
designation of, 182, 183 ; 
division of, 183, 184, 219 ; 
junction-stars of, 184, 210, 211, 220 r 

lords of, 109 ; 

meaning of Indian, 182, 210, 211 , 
names of-general 210, 211, 263 ; 
„ Tamil, 109; 
„ „ -Yajur Vedic with presiding 
deities, 220 ; 
number of, 182 ; 
Kg- Vedic, 183 ; 

shifting of the beginning of, 18, 19 ; 

starting of 182, 183 
Nandsa Yupa inscription, 254 
Napolean Bonaparti, 168 
Narseh, Sassanid king, 232 



National Observatory, 5, 8, 12, 14 
Nautical Almanac, 3, 165 
Nepthys, 164 

Neugebauer, O., 3, 160, 175, 185, 189, 192, 

198, 199, 201, 203, 204 
New Testament, 169 
Newton, Isaac, 2, 193, 206, 240, 259 ; 

precession of the equinoxes, 207 
Night, definition of, 157 
Nile flood, 158, 164, 165, 174, 189 
Nineteen-year cycle, 176, 200 
Nirayaua, 259, 260, 262, 268 
Nirt,iaya Sindhu, 101 
Nirukta, 214 

Nirvana, Buddha, 235, 257 

Nisan, 161, 170, 175, 178, 179, 229 

Nisitha, 108 

Nodes, 185, 186, 187, 269 

Nona, 159 

Nones, 168 

Numa Pompilius, 168 
Nut, 164 
Nutation, 209 
Nychthemeron, 157, 159 

Obliquity, of the ecliptic, 158, 191, 207, 208, 225 
amount of, 191 ; 
definition of , 191 ; 
^Vctaeteris, 176 
Octavious Caesar, 168 ; 
Odyssey, 201 
Olympiads, 178 
Omar Khayyam, 166, 172, 240 
Omina, 19,3, 235 
Orbit, of the earth, 207 
Orion, 189 
Orion, 190, 195 
Osiris, Egyptian god, 164 

Paikuli (inscription), 232 
Paitamaka Siddhanta, 223 
Paja (inscription), 229 
Pakaa, 227-231 ; 

krsna or vahula, 15, 221, 228, 233, 247 ; 

iukla, 15, 221, 228, 247 ; 
Pala, 160 
Palas, 257 
Pallavas, 256 
Pancangas,. list of, 21, 22 

Panca Siddhlntifca of Varahamihira, 158, 162, 

197,223,226, 236, 237, 238 
Panemos, Greek month, 230 

Panjtar (inscription), 229 
Pannekoek, Dr. Anton, I'M, 176,178.185,194, 
196, 197 

Paraviddha, 101, 108 ; rules for, 109 
Parivatsara, 225 
Passpv^r last, 170 
Pataliputra, 10, 213, 234, 252. 
Paultia Siddkinta^ffli 
Paulus of Alexandriav204* 23? 
Perihelion, 242*, mbkfem^m.t of j.S*3 
Peshawar Museum (inscription), 229. 230 
Philhellens, 213 

Phraates 1, 213 

Pictorial Astronomy, 194, 195 
PUlai, a K., 101, 223 
Pingala, 214 

Planet, 169 ; order of distance, 203 ; 

references in Rg-Veda, 212 ; 
Planetarium, 203 

Planetory Astrology, 169, 194—196 
Plato, 202, 203, 228, 229 ; geometry, 202 
Pleiades, 182, 190, 195, 199, 219 
Polar axis, 208 

Polaris {< Ursae Minoris), 190, 207, 239 
Pole, celestial, 191, 192, 207 ; 

definition of, 191 ; 

motion of, 207 ; 

observation of, 190, 191 ; 

precessional path of, 207 
Pope, Gregory XIII, 159, 172 
Pradosavrata, 108 
Prahara, 160 
Prajapati, 217 

Prana (division of time), 160 
Pratali, 108 

Precession of the equinoxes, 2, 7, 8, 193, liOO, 

204-206, 237, 238, 240, 253, 259, 267 ; 

Al-Baftani's rate of, 206 ; 

among Hindus, 226 ; 

among Indian astronomers, 267 ; 

amplitude of precessional oscillation 
according to S. S., 268 ; 

Bhaskariicarya's rate of, 269 ; 

consequences of, 205, 206 ; 

discovery of, 204, 205 ; 

effect in Indian calendar, 7, 11, 18 ; 

effect in Indian Siddhfuitas, 226 ; 

explanation by Neffton, 207, 208 ; 

Hipparchos's rate of, 205 ; 

motion of (precessional), 208, 268 ; 

Munjala Bhata's rate of, 268 ; 

numerical value of, 209 ; 

physical explanation of, 207, 208 ; 

Prthudaka Svaml's rate of, 268 ; 

Ptolemy's rate of, 205 206 ; 

rate of annual, 209 ; 

rate of lunar, 208, 209 ; 

rate of solar, 208, 209 ; 

Surya Siddhanta's rate of, 268 
Prthudaka Svami, 259, 268, 269 
Proclos, on precession, 206 
Ptolemy, Claudius, 161, 165, 166, 177, 178, 185, 

192, 200, 201, 203-206, 214, 228, 238, 24C, 

263, 266 ; 

on astrology, 205 ; 

„ evection, 204 ; 

„ rate of precession, 205 ; 

„ theory of planetary motion, 204 ; 
Ptolemies, 213 
Ptolemy, Euergetes, 165 
Pulakesin I, 233 
Pulakesb -It,'35ff 
Pulastya, 236 
Puranas, 101, 252 

Purnimfinta; moath, 157, 227,, 230, 231, 2S3, 

247, 256 
Puruspur, 232 
Purvahna, 101, 108 
PurvavidttBa^Wt,a08-p«iA» *rt?3fl9 

Puskalavati, 230 

Pythagorean number, 198 ;(fig.) 

Quartz clock, 12, 159 
Questionnaire, regarding calendar, 22 ; 
replies to, 23-31 

Ha, Egyptian sun-god, 164 
Kahu, ascending node, 186 
Ramaya^ta, 261 
Kampurva (inscription), 227 
Rahganatha, 233 
Kapson, 255 

Refraction, 225, 226 ; effect of, 225 
Retrograde motion, 169, 194, 195 
-ttg-Samhita, 217, 218 

Biy-Vedas,V&, 212, 214, 216, 217, 218, 221, 
222 ; 

calendaric references in, 216-218 ; 
description of, 215 ; 
Ribhus, 216 

Right ascension, 192, 204 

Riza Shah Pahlavi ; 167 

Romaka, 236,*239 

Rome, Era of foundation of, 178 

Rotation of the earth, 157, 158 

Rudiadanian, 233 

Rudra Simha,' baka satrap, 231, 236 

Sachs, A., 199, 201 

Saha, Prof. M. N„ 173, 232, 252, 256 

Sahdaur A (inscription), 229 

Sahdaur B (inscription), 229 

Sahni, Dayaram, 232 

6akas, 213, 230, 233, 236 

Sakadvipl Brahmanas, 214, 236, 256 

6a k a samvat, 2o5 

fiakasthan, 213. 233 

6akendra kala, 255 

£alivahana &aka, 255 

Samarkand, 10 

Sama Veda, 214, 218 

Samhitas, 214, 218 

Samkranti, 2, 7, 239, 244 ; 

Mahavisuva, 215 ; 

Makara, 215 

rules of, 244, 247, 259 ; 

Uttarayana, 215 j 
Sampat calana, 269 
Samudragupta* 255 
Samvatsara, 255, 270 
Sangava, 108 
6anku (gnomon), 188 
6ara (celestial latitude), 262 
.Sargon I, 215 
Saros, 184, 185, 202,217 
Sarton, George, 159, 188, 203, 204, 206 
Wastry, Mm. ;Bapudev, 259 
pastry, Prof. Mm. Bidhusekhar, 235 
fSatakarni, 228, 233 
(Satananda, 160 

Satapatha Brahma^a, 18, 189, 219 
^yljha^aa, 212+213, 227-231, 233, 234, 255, 
Saturn, planetx,^, 195, 203^239 



Saura day, 197 

S&vana, 2, 157, 223, 224 
S&yahna, 106 

Sayana, 1, 11, 12, 13, 217, 259 
Bcaliger, Joseph, 9, 11, 161 
Scaliger, Julius, 162 
Schmidt, Dr. Olaf, 163 
Schrader, 215 
Scientific American, 190 
Scorpion, 193, 195, 198 
Scythian Period of Indian History, 232, 255 
Seasons, 157, 158, 174, 189, 216, 217, 227,230, 239 
causes of, 259 ; 

determination by gnomon, 189 
error in counting, 260 ; 
length of, 174, 175, 261 ; 
moving back of, 18 ; 
names of Indian, 217, 241, 260 ; 
position of, 1, 6, 260 ; 

relation of months with seasons in Vedic 
age, 216, 218 ; 

in £g-Veda, 216, 217 
Seb, Egyptian god 164 
Seleucus, 178, 213, 228 
Senas, Hindu ruling dynasty, 257 
Seneca, 225 

Sengupta, P. C, 183, 215, 221, 227, 238, 253, 

Set, Egyptian god, 164 
Sewell, K. S., 246 
Sezta, 159 

Shahpur I (Sassanid king), 232 
Shama Sastry, Dr. R., 223, 224 
Shin Kot (inscription), 229 
Siddhanta Jyotisa, 161, 221 
Siddhantas, 1, 2, 3, 163, 234, .236,237, 238, 

Arya,238, 242,251; 

Brahma, 238, 242, 251 ; 

definition of, 234 ; 

Paitamaha, 236-238 ; 

Paulisa, 236-238 ; 

Roinaka, 236, 237, 240 ; 

Surya, 236, 238-244 ; 

Vasistha, 236, 237 
Siddhanta Bokhara of 6rlpati, 162 
Si<* V-Sada Siromatii of Bbaskaracarya, 238, 


Sidereal time, 158 

Signs, of the zodiac, 192, 193, 194, 196, 206, 

223, 224, 237, 239, 240 
foksa, 214 

Sircar, 1>.C.,22*. 231, 233, 234 

Sirius, 104 

givaratri, 108 

Sky and Telescope, 177 

Solar day, mean, 157, 158 ; 

division of, 159 ; 

Solar cycle, 162 ; 
Solar time, mean, 158 ; 
Solstices, 188, 189, 226 ; 

determination by Vedic Hindus, 266 ; 

observation in Aitareya Brahmana, 266 

summer, 188, 189- 192, 226, 266 ; 

winter, 13, 189, 192, 223, 224, 226, 241, 
259 ; 

Solstitial colure, 226 

Somakara, 222 
Soaigenes, 168 
Sothic cycle, 165 
grlpati. 11,246 

Srlsena, 237 ; on precession, 267 

Stone-henge, 189, 190 

gudi, 247, 248 

Suddha, 7, 247 

Sui Vihar (inscription), 230 

Sulva-Sutras, 190, 214 

Sun, distance from the earth, 208 ; 

entry into naksatras, 15, 40 ; 

mass of, 208 ; 

mean daily motion, 197 ; 

semi-diameter of, 225 
Sun-dial, 159 
Sun-rise, 15 ; 

timings of certain important places, 116 
Sun-set, 15 

timings of certain important places, 116 ; 
Sunga, 213, 228, 235 
Surya Pra/napti, 223 

Surya Siddhanta, 1, 2, 158, 189, 192, 203, 214, 

236-240, 242-46, 250, 251, 253, 262-264, 

267, 268, 270 ; 

calendar in, 239, 240 ; 

description of, 238, 244 ; 

error in length of year, 2, 241 ; 

length of the year, 2, 240, 241 ; 

star positions of, 264, 205 ; 

theory of trepidation, 268 
Sutras, 214. 215, 221 ; 

Srauta. Urhya, Dharma, Sulva, 214 
Synodic period, 158, 175, 182 ; 

revolution of planets acc. to P. S., 197 
Syntaxis or Almagest, 192, 201, 203, 204 

Taittiriya Brahmana, 182 ; 

Taittirlya Samhita, 218, 220, 221, 260 

Takht-i-Bahi (inscription), 229 

Tantra, 163 

Tarn, 229, 255 

Jaxila, 213, 228, 230, 256 

Taxila copper plate (inscription), 229 

Taxila silver scroll (inscription), 229 

Taxila silver vase (inscription), 229 

Telephos of Kapsa, 230 t 

Tertia, 159 

Tetrabibhs, 201, 204, 205 
Thabit-ibn-Qurra, 206 
Thales of Miletus, 202 

prediction of solar eclipse, 202 ; 
Theaitetus of Athens, 202 ; 
Thcon of Alexandria, 204, 206, 240 ; 

on trepidation, 206, 240 
Thibaut, Dr. G., 197, 223, 225, 237 
Thirteen- month calendar, 171 
Thoth, Egyptian god, 164 
Tigris, river, 157 
Tilak, B. G., 11, 189, 215, 216 
Time, natural divisions of, 157-160 
Timocharis, 205 
Tiridatcs, 178 
Tisya, 217, 227 

Tithi. 183, 218, 227, 228, 230, 234, 236, 248 ; 
average duration of, 221, 222, 224, 248 ; 
comparison of Siddhantic and modern, 3 
defined, 3, 221 ; 

definition in Aitareya Brahmana, 221 ; 

„ „ Siddhantas, 221 ; 

,, ,, Vedanga Jyotisa, 224, 225 ; 

duration of Vedic tithi, 221 ; 
error in the old method, 3, 14 ; 
lords of, 109 ; 
measurement of, 248 ; 
names of, 222 ; 
numbers of, 15, 221, 222 
Tiihitatvam, 101 

Trepidation, theory of, 204, 206, 207,238, 240, 

259, 268, 269 
Tuladi, 239 
Tycho Bvahe, 206 

Ullulu, 170 
Ulugh Begh, 10 
Umbra Extensa, 204 
Umbra Versa, 204 
Und (inscription), 231 
Upanisads, 214, 215 
Urcmometry, 205 
Usavadata, Saka prince, 233 
Ua-alafotlika, 101 
Utkramajya, 204 

Uttarfiyana. 189, 219, 224, 22G, 239, 260 

Vadi, 247, 248 

Vaidya, Prof. R.V., 203 

I Vt i dynna tht Di hs i f lyan h 101 

Vajasancyi Swihhita, 218 

Vajheska, 231 

Van dcr Waerdcn , 160 

Varahamihira, 2, 7, 192, 193, 197, 223, 226, 236, 

237, 238, 240, 252, 255, 267 
Varuna, Indian god, 215, 216 
Vasistha, Indian sage, 236 
Vasistha Siddhanta, 236, 237, 267 
Vasudcva I, 231, 232 
Vasudcva II, 231, 232 
Vedas, description and literature, 214 ; 

age of its literature, 214, 215 
Vedfingas, 214, 215 

Vedanga Jyotisa, 101, 217, 224, 226, 237, 240, 


■description of, 221-225 
Vehsadjan, 232 
Ventris, 202 

Venus, planet, 194, 195, 198, 203, 239 ; 

heliacal rising and setting of, 6, 15 
( sec also Calendar for five years). 
Vernal equinox, 2, 158, 226, 239, 241, 267 
Vernal point, 1, 158, 205 ; 

movement of, 193, 194, 205, 267 
Vespers, 159 

Vidyasagar, Pandit Ishwar Chandra, 260 
Vighati, 160 
Vikramaditya, 254, 255 
Viksepa, 192,262-265,267 
Virapurusadatta, 228 



Visnu Candra,:237 ; on precession, 267 
Visuvfin, 216, 219, 221, 266 
Viguvansa, 262 
Vogt, 203 
Vrddha Garga, 252 
Vyakarana, 214 

Wardak (inscription), 230 

Water-clock, 157, 159 

Webster, A. G., 207, 208 

Week, 169, 170, 203, 223, 234. 251, 252 ; 

origin and invention of, 169, 170 
Winternitz, 214, 215, 218 
World Calendar Association, 10, 12, 171 
Worlds' day, 172, 173 

Yajnavalkya Vajasaneya, 218 
Yajur Veda, 182, 183, 214, 218-222 ; 

Black, 218; 

6ukla, 218 
Yajurveda Samhita, 218 
Yajus Jyotisa, 222 
Yama, division of day, 160 
Yamakoti, 239 
Yamardha. 108 
Yaska, 214 
Yavanapuri, 237 
Yavanas, 213, 256 

Year, 216 ; beginning of, 1, 4, 6, 13, 175 ; 
beginning of in Brahmanas, 241, 245 ; 
beginning of lunar. 221 ; 

"in Paitamaha, 223 ; 
*' in S. S., 239 
" religious calendar , 251 ; 
" Siddhantic, 11, 241, 245 ; 
" Solar, 2, 241 ; 
" " Vedanga Jyotisa, 241, 245 ; 

" Vedic Aryan, 216, 218 ; 
definition of, 157, 158 ; 
draconitic (eclipse), 186 ; 
error in beginning of, 1, 13, 15, 241 ; 
error in beginning of Indian solar, 2 ; 
first month of, 4, 6, 241, 242, 251 ; 
Jovian (Barhaspatya), 270 ; 
length (average) of Babylonian, 161, 177 ; 
length of as foundby ancient astronomers, 
174, 261 ; 
" Brahmagupta, 162 ; 
" Gregorian, 12, 13 ; 
" " Paitamaha, 223, 240 ; 
" " Ptolemy, 240 ; 
" " sidereal, 158, 205, 240, 246 ; 
" 55 solar, 223 ; 

*' " Surya Siddhanta, 2,240, 241, 246'. 
" " tropical, 1, 2, 4, 12, 158, 174, 175, 
205, 240, 246 ; 
" Varahamihira, 240 ; 
*** " Vedic Aryan, 216 ; 

Year— contd. 

starting day of the solar, 241 
Yoga, names and lords of, 110 ; 

calculation of, 110 
Yogatara (junction star), 183, 184, 210, 211 
Yuga, 217 ; 

ofEomaka Siddhanta 237 

of Vedanga Jyotisa, 223, 224 ; 
Yugadi, 107 

Zarathustra, 167 

Zeda (inscription), 230, 231 

Ziggurat, 196 

Zinner, Dr. Ernest, 164, 196 
Zodiac, definition of, 192, 193, 202 ; 
first point of , 14 ; 
lunar, 182, 183, 223, 226 ; 
Arabian, 182, 183 ; 
Chinese, 182, 183 ; 
Indian ( see naksatra) 
place of origin, 183 ; 
Kg Vedic, 217 ; 
position through ages, 200 ; 
signs of the, 193 ; 
starting point of, 193 ; 
zero point of the Hindu, 262, 266, 287 f 

Zodiacal signs, different names of, 193/see also 
signs of the zodiac).